A091055 Expansion of x*(1-2*x)/((1-x)*(1+2*x)*(1-6*x)).

0, 1, 3, 23, 127, 783, 4655, 28015, 167919, 1007855, 6046447, 36280047, 217677551, 1306070767, 7836413679, 47018503919, 282110979823, 1692665966319, 10155995623151, 60935974088431, 365615843831535, 2193695064387311

Offset: 0

Author

Paul Barry, Dec 17 2003

Keywords

• easy
• nonn

Comments

Number of walks of length n between adjacent vertices of the Johnson graph J(5,2).

6^n = A091054(n) + 6*a(n) + 3*4*A091056(n).

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Eric Weisstein's World of Mathematics, Johnson Graph
• Index entries for linear recurrences with constant coefficients, signature (5,8,-12).

Crossrefs

Cf. A091054, A091056.

Programs

GAP

List([0..30], n-> (3*6^n -5*(-2)^n +2)/30); # G. C. Greubel, Dec 27 2019

Magma

[(3*6^n -5*(-2)^n +2)/30: n in [0..30]]; // G. C. Greubel, Dec 27 2019

Magma

R:=PowerSeriesRing(Integers(), 25); [0] cat  Coefficients(R!( x*(1-2*x)/((1-x)*(1+2*x)*(1-6*x)))); // Marius A. Burtea, Dec 30 2019

Maple

seq( (3*6^n -5*(-2)^n +2)/30, n=0..30); # G. C. Greubel, Dec 27 2019

Mathematica

Table[(3*6^n -5*(-2)^n +2)/30, {n,0,30}] (* G. C. Greubel, Dec 27 2019 *)

PARI

vector(31, n, (3*6^(n-1) -5*(-2)^(n-1) +2)/30) \\ G. C. Greubel, Dec 27 2019

Sage

[(3*6^n -5*(-2)^n +2)/30 for n in (0..30)] # G. C. Greubel, Dec 27 2019

Formula

a(n) = (3*6^n - 5*(-2)^n + 2)/30.

E.g.f.: (3*exp(6*x) - 5*exp(-2*x) + 2*exp(x))/30. - G. C. Greubel, Dec 27 2019