A091054 Expansion of (1 - 5*x - 2*x^2) / ((1 - x)*(1 + 2*x)*(1 - 6*x)).

1, 0, 6, 18, 138, 762, 4698, 27930, 168090, 1007514, 6047130, 36278682, 217680282, 1306065306, 7836424602, 47018482074, 282111023514, 1692665878938, 10155995797914, 60935973738906, 365615844530586, 2193695062989210

Offset

0,3

Comments

Closed walks of length n at a vertex of the Johnson graph J(5,2).

6^n = a(n) + 6*A091055(n) + 3*4*A091056(n).

Links

Colin Barker, 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).

Formula

a(n) = (6^n + 5*(-2)^n + 4)/10.

a(n) = 5*a(n-1) + 8*a(n-2) - 12*a(n-3) for n>2. - Colin Barker, Dec 26 2019

E.g.f.: (exp(6*x) + 5*exp(-2*x) + 4*exp(x))/10. - G. C. Greubel, Dec 27 2019

Maple

seq( (6^n +5*(-2)^n +4)/10, n=0..30); # G. C. Greubel, Dec 27 2019

Mathematica

Table[(6^n +5*(-2)^n +4)/10, {n, 0, 30}] (* G. C. Greubel, Dec 27 2019 *)
LinearRecurrence[{5, 8, -12}, {1, 0, 6}, 30] (* Harvey P. Dale, Oct 21 2021 *)

Prog

(PARI) Vec((1 - 5*x - 2*x^2) / ((1 - x)*(1 + 2*x)*(1 - 6*x)) + O(x^25)) \\ Colin Barker, Dec 26 2019
(PARI) vector(31, n, (6^(n-1) +5*(-2)^(n-1) +4)/10) \\ G. C. Greubel, Dec 27 2019
(Magma) [(6^n +5*(-2)^n +4)/10: n in [0..30]]; // G. C. Greubel, Dec 27 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 25); Coefficients(R!( (1 - 5*x - 2*x^2) / ((1 - x)*(1 + 2*x)*(1 - 6*x)))); // Marius A. Burtea, Dec 29 2019
(Sage) [(6^n +5*(-2)^n +4)/10 for n in (0..30)] # G. C. Greubel, Dec 27 2019
(GAP) List([0..30], n-> (6^n +5*(-2)^n +4)/10); # G. C. Greubel, Dec 27 2019

Crossrefs

Cf. A091055, A091056.

Sequence in context: A003496 A009582 A222913 * A012774 A306656 A027744

Adjacent sequences: A091051 A091052 A091053 * A091055 A091056 A091057

Keyword

easy,nonn

Author

Paul Barry, Dec 17 2003

Status

approved