A123894 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).

1, 5, 25, 115, 525, 2405, 11025, 50525, 231525, 1060979, 4862065, 22280875, 102104045, 467901065, 2144199765, 9825991725, 45028504525, 206347239279, 945605099381, 4333321849875, 19857843661645, 91000384646845, 417017585036185, 1911021221349165

Offset

0,2

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

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

A. Burstein and T. Mansour, Words restricted by 3-letter generalized multipermutation patterns, arXiv:math/0112281 [math.CO], 2001; Annals. Combin., 7 (2003), 1-14.

Index entries for linear recurrences with constant coefficients, signature (5,-10,40,-35,105,-50,100,-24,24).

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]^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

Crossrefs

Cf. A005251, A123892, A123893, A225685.

Sequence in context: A089947 A267467 A123890 * A200781 A055297 A244828

Adjacent sequences: A123891 A123892 A123893 * A123895 A123896 A123897

Keyword

nonn,easy

Author

N. J. A. Sloane, Nov 20 2006

Status

approved