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Revision History for A224810

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A224810

Subsets of {1,2,...,n-6} without differences equal to 3 or 6.
(history; published version)

#26 by Ray Chandler at Wed Sep 04 09:55:47 EDT 2024

STATUS

editing

approved

#25 by Ray Chandler at Wed Sep 04 09:55:42 EDT 2024

LINKS

<a href="/index/Rec#order_24">Index entries for linear recurrences with constant coefficients</a>, signature (1, 0, -1, 2, 0, -2, 4, 0, 2, 2, 0, 4, -2, 0, 2, -4, 0, -2, -2, 0, -1, -1, 0, -1).

STATUS

approved

editing

#24 by N. J. A. Sloane at Sun Apr 30 22:42:41 EDT 2017

STATUS

proposed

approved

#23 by G. C. Greubel at Sun Apr 30 21:44:55 EDT 2017

STATUS

editing

proposed

#22 by G. C. Greubel at Sun Apr 30 21:44:45 EDT 2017

COMMENTS

a(3*k) = (A000930(k))^3,

a(3*k+1) = (A000930(k))^2 * A000930(k+1),

a(3*k+2) = A000930(k) * (A000930(k+1))^2

LINKS

G. C. Greubel, <a href="/A224810/b224810.txt">Table of n, a(n) for n = 0..1000</a>

FORMULA

a(3*k) = (A000930(k))^3.

a(3*k+1) = (A000930(k))^2 * A000930(k+1).

a(3*k+2) = A000930(k) * (A000930(k+1))^2.

MATHEMATICA

CoefficientList[Series[(1 + x^3 - x^4 - x^5 + x^6 - 2*x^7 - x^8 - x^9 - 2*x^10 - x^12 - x^13 - x^15)/((1 - x)*(1 + x + x^2)*(1 - x - x^3)*(1 + 3*x^3 + 7*x^6 + 9*x^9 + 7*x^12 + 3*x^15 + x^18)), {x, 0, 50}], x] (* G. C. Greubel, Apr 30 2017 *)

PROG

(PARI) x='x+O('x^50); Vec((1 + x^3 - x^4 - x^5 + x^6 - 2*x^7 - x^8 - x^9 - 2*x^10 - x^12 - x^13 - x^15)/((1 - x)*(1 + x + x^2)*(1 - x - x^3)*(1 + 3*x^3 + 7*x^6 + 9*x^9 + 7*x^12 + 3*x^15 + x^18))) \\ G. C. Greubel, Apr 30 2017

STATUS

approved

editing

#21 by Ralf Stephan at Mon May 20 04:38:51 EDT 2013

STATUS

editing

approved

#20 by Ralf Stephan at Mon May 20 04:36:23 EDT 2013

NAME

Number of permutations (p(1), p(2), ..., p(n)) satisfying -k <= p(i)-i <= r and p(i)-i not in the set I, i=1..n, with k=3, r=6, I={-2,-1,1,2,3,4,5}.

Subsets of {1,2,...,n-6} without differences equal to 3 or 6.

COMMENTS

Number of subsets of {permutations (p(1,), p(2,), ..., p(n)) satisfying -k <= p(i)-i <= r and p(i)-6} without differences equal to i not in the set I, i=1..n, with k=3 or , r=6, I={-2,-1,1,2,3,4,5}.

STATUS

proposed

editing

Discussion

Mon May 20

04:38

Ralf Stephan: I exchanged the title with the definition in the comment, which is more crisp and descriptive.

#19 by Vladimir Baltic at Sat May 18 14:58:07 EDT 2013

STATUS

editing

proposed

#18 by Vladimir Baltic at Sat May 18 14:57:50 EDT 2013

COMMENTS

a(3*k-1) = (A000930(k))^3,

a(3*k+1) = (A000930(k))^2 * A000930(k+1),

a(3*k+12) = A000930(k) * (A000930(k+1))^2

STATUS

proposed

editing

#17 by Vladimir Baltic at Sat May 18 14:00:59 EDT 2013

STATUS

editing

proposed