STATUS
reviewed
approved
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Revision History for A123894
(Bold, blue-underlined text is an addition; faded, red-underlined text is aShowing entries 1-10 | older changes
Expansion of g.f.: (1+x^2)*(1+2*x^2)*(1+3*x^2)*(1+4*x^2)/(1-5*x+10*x^2 -40*x^3+35*x^4-105*x^5 +50*x^6-100*x^7+24*x^8-24*x^9).
(history; published version)
(history; published version)
STATUS
proposed
reviewed
STATUS
editing
proposed
COMMENTS
Number of words of length n over ({0,1,2,3,4} which have no factor iji with i>j. - N. J. A. Sloane, May 21 2013
STATUS
approved
editing
PROG
(MAGMAMagma) R<x>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+x^2)*(1+2*x^2)*(1+3*x^2)*(1+4*x^2)/(1-5*x+10*x^2 -40*x^3+35*x^4-105*x^5 +50*x^6-100*x^7+24*x^8-24*x^9) )); // G. C. Greubel, Aug 06 2019
STATUS
proposed
approved
STATUS
editing
proposed
NAME
GExpansion of g.f.: -(1+x^2)*(1+2*x^2)*(1+3*x^2)*(1+4*x^2)/(-1-5*x+10*x^2-35*x^4-50*x^6 -24*x^8+5*x+40*x^3+35*x^4-105*x^5 +50*x^6-100*x^7+24*x^8-24*x^9).
LINKS
G. C. Greubel, <a href="/A123894/b123894.txt">Table of n, a(n) for n = 0..1000</a>
FORMULA
G.f. may be written more symmetrically as 1/(1-x*(1 +1/(1+x^2) +1/(1+2*x^2) +1/(1+3*x^2) +1/(1+4*x^2))). - N. J. A. Sloane, May 21 2013
MAPLE
seq(coeff(series((1+x^2)*(1+2*x^2)*(1+3*x^2)*(1+4*x^2)/(1 -5*x +10*x^2 -40*x^3+35*x^4-105*x^5+50*x^6-100*x^7+24*x^8-24*x^9), x, n+1), x, n), n = 0 .. 30); # G. C. Greubel, Aug 06 2019
MATHEMATICA
CoefficientList[1/(1 - x(1 + 1/(1+x^2) + 1/(1+2x^2) + 1/(1+3x^2) + 1/(1+4x^2))) + O[x]^24, 30, x] (* Jean-François Alcover, Jan 09 2019 *)
PROG
(PARI) my(x='x+O('x^30)); Vec((1+x^2)*(1+2*x^2)*(1+3*x^2)*(1+4*x^2)/(1 -5*x +10*x^2 -40*x^3+35*x^4-105*x^5+50*x^6-100*x^7+24*x^8-24*x^9)) \\ G. C. Greubel, Aug 06 2019
(MAGMA) R<x>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+x^2)*(1+2*x^2)*(1+3*x^2)*(1+4*x^2)/(1-5*x+10*x^2 -40*x^3+35*x^4-105*x^5 +50*x^6-100*x^7+24*x^8-24*x^9) )); // G. C. Greubel, Aug 06 2019
(Sage) ((1+x^2)*(1+2*x^2)*(1+3*x^2)*(1+4*x^2)/(1-5*x+10*x^2-40*x^3 +35*x^4-105*x^5 +50*x^6-100*x^7+24*x^8-24*x^9)).series(x, 30).coefficients(x, sparse=False) # G. C. Greubel, Aug 06 2019
(GAP) a:=[1, 5, 25, 115, 525, 2405, 11025, 50525, 231525];; for n in [10..30] do a[n]:=5*a[n-1]-10*a[n-2] +40*a[n-3]-35*a[n-4]+105*a[n-5] -50*a[n-6]+100*a[n-7]-24*a[n-8]+24*a[n-9]; od; a; # G. C. Greubel, Aug 06 2019
STATUS
approved
editing
STATUS
proposed
approved
STATUS
editing
proposed