A246986 Expansion of (1-5*x+6*x^2-x^3)/((1-x)*(1-2*x)*(1-3*x)*(1-4*x)).

1, 5, 21, 84, 331, 1300, 5111, 20144, 79611, 315420, 1252351, 4980904, 19837091, 79086740, 315557991, 1259856864, 5032285771, 20107685260, 80366302031, 321271760024, 1284506433651, 5136283390980, 20539905484471, 82143935602384, 328528679208731, 1313973518843900, 5255470464625311, 21020610992695944

Offset

0,2

Links

Todd Silvestri, Table of n, a(n) for n = 0..1660

A. Prasad, Equivalence classes of nodes in trees and rational generating functions, arXiv:1407.5284 [math.CO], 2014.

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

Formula

a(n) = (3^(n+1)+7*4^n-3*2^n-1)/6. - Todd Silvestri, Nov 16 2014

Mathematica

a[n_Integer/; n>=0]:=(3^(n+1)+7*4^n-3*2^n-1)/6 (* Todd Silvestri, Nov 16 2014 *)
CoefficientList[Series[(1 - 5 t + 6 t^2 - t^3) / ((1 - t) (1 - 2 t) (1 - 3 t) (1 - 4 t)), {t, 0, 40}], t] (* Vincenzo Librandi, Nov 16 2014 *)
LinearRecurrence[{10, -35, 50, -24}, {1, 5, 21, 84}, 30] (* Harvey P. Dale, May 12 2017 *)

Prog

(Magma) [(3^(n+1)+7*4^n-3*2^n-1)/6: n in [0..30]]; // Vincenzo Librandi, Nov 16 2014
(PARI) Vec((1-5*x+6*x^2-x^3)/((1-x)*(1-2*x)*(1-3*x)*(1-4*x)) + O(x^30)) \\ Michel Marcus, Jan 14 2016

Crossrefs

Sequence in context: A026027 A002054 A289797 * A272547 A247001 A271157

Adjacent sequences: A246983 A246984 A246985 * A246987 A246988 A246989

Keyword

nonn,easy

Author

N. J. A. Sloane, Sep 15 2014

Status

approved