A021234 Expansion of 1/((1-x)(1-2x)(1-7x)(1-10x)).

1, 20, 277, 3324, 37149, 398916, 4181269, 43157708, 440992717, 4475837652, 45219751941, 455427151452, 4576878947005, 45927041513828, 460378179477493, 4611536145214956, 46169641905360813, 462076382226349044

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Index entries for linear recurrences with constant coefficients, signature (20,-123,244,-140).

Formula

a(n) = (5*10^(n+3) - 12*7^(n+3) + 27*2^(n+3) - 20)/1080. [Yahia Kahloune, Jul 07 2013]

a(0)=1, a(1)=20, a(2)=277, a(3)=3324; for n>3, a(n) = 20*a(n-1) -123*a(n-2) +244*a(n-3) -140*a(n-4). - Vincenzo Librandi, Jul 08 2013

a(0)=1, a(1)=20; for n>1, a(n) = 17*a(n-1) -70*a(n-2) +2^n -1. - Vincenzo Librandi, Jul 08 2013

Mathematica

CoefficientList[Series[1 / ((1 - x) (1 - 2 x) (1 - 7 x) (1 - 10 x)), {x, 0, 20}], x] (* Vincenzo Librandi, Jul 08 2013 *)
LinearRecurrence[{20, -123, 244, -140}, {1, 20, 277, 3324}, 20] (* Harvey P. Dale, Aug 12 2023 *)

Prog

(Magma) I:=[1, 20, 277, 3324]; [n le 4 select I[n] else 20*Self(n-1)-123*Self(n-2)+244*Self(n-3)-140*Self(n-4): n in [1..25]]; /* or */ m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)*(1-2*x)*(1-7*x)*(1-10*x)))); // Vincenzo Librandi, Jul 08 2013

Crossrefs

Sequence in context: A004334 A019483 A018056 * A021474 A017999 A244653

Adjacent sequences: A021231 A021232 A021233 * A021235 A021236 A021237

Keyword

nonn,easy

Author

N. J. A. Sloane.

Status

approved