Revision History for A204686
(Underlined text is an addition;
strikethrough text is a deletion.)
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#7 by Russ Cox at Fri Mar 30 18:37:34 EDT 2012
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| AUTHOR
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_Paul D. Hanna (pauldhanna(AT)juno.com), _, Jan 18 2012
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Discussion
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| Fri Mar 30
| 18:37
| OEIS Server: https://oeis.org/edit/global/213
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#6 by T. D. Noe at Wed Jan 18 12:07:13 EST 2012
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#5 by Paul D. Hanna at Wed Jan 18 09:49:26 EST 2012
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#4 by Paul D. Hanna at Wed Jan 18 09:49:24 EST 2012
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| NAME
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G.f.: A(x) = Sum_{n>=0} x^n * A(x)^A006068(n) where A006068 forms the inverse permutation of the binary Gray code numbers. (A003188).
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| COMMENTS
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A006068 satisfies: A006068(n) XOR [A006068(n)/2] = n.
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| EXAMPLE
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G.f.: A(x) = 1 + x + 2*x^2 + 6*x^3 + 18*x^4 + 62*x^5 + 228*x^6 +...
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| PROG
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((PARI) {A006068(n)=local(B=n); for(k=1, floor(log(n+1)/log(2)), B=bitxor(B, n\2^k)); B}
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| CROSSREFS
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Cf. A192483, A006068, A003188.
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| STATUS
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proposed
editing
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#3 by Paul D. Hanna at Wed Jan 18 08:34:04 EST 2012
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#2 by Paul D. Hanna at Wed Jan 18 08:33:47 EST 2012
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| NAME
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allocated for Paul D. Hanna
G.f.: A(x) = Sum_{n>=0} x^n * A(x)^A006068(n) where A006068 forms the inverse permutation of the binary Gray numbers.
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| DATA
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1, 1, 2, 6, 18, 62, 228, 869, 3410, 13663, 55689, 230276, 963851, 4076429, 17394641, 74798044, 323797908, 1409980003, 6171824159, 27141256911, 119854448404, 531261779875, 2362873352568, 10541865261557, 47165485163426, 211572830443060, 951338664998601, 4287174496933723
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| OFFSET
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0,3
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| COMMENTS
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A006068 satisfies: A006068(n) XOR [A006068(n)/2] = n.
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| EXAMPLE
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G.f.: A(x) = 1 + x + 2*x^2 + 6*x^3 + 18*x^4 + 62*x^5 + 228*x^6 +...
The g.f. A(x) satisfies:
A(x) = 1 + x*A(x) + x^2*A(x)^3 + x^3*A(x)^2 + x^4*A(x)^7 + x^5*A(x)^6 + x^6*A(x)^4 + x^7*A(x)^5 + x^8*A(x)^15 + x^9*A(x)^14 + x^10*A(x)^12 +...
where the powers of A(x) are given by A006068, which begins:
[0,1,3,2,7,6,4,5,15,14,12,13,8,9,11,10,31,30,28,29,24,25,27,26,...].
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| PROG
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(PARI) {A006068(n)=local(B=n); for(k=1, floor(log(n+1)/log(2)), B=bitxor(B, n\2^k)); B}
{a(n)=local(A=1+x); for(i=1, n, A=sum(m=0, n, x^m*(A+x*O(x^n))^A006068(m))); polcoeff(A, n)}
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| CROSSREFS
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Cf. A192483, A006068, A003188.
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| KEYWORD
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allocated
nonn
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| AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Jan 18 2012
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| STATUS
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approved
editing
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#1 by Paul D. Hanna at Wed Jan 18 08:21:55 EST 2012
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| NAME
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allocated for Paul D. Hanna
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| KEYWORD
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allocated
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| STATUS
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approved
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