A021129 Expansion of 1/((1-x)(1-2x)(1-5x)(1-8x)).

1, 16, 175, 1650, 14481, 122316, 1010995, 8250550, 66817861, 538611216, 4329233415, 34735589850, 278393339641, 2229689837716, 17850234337435, 142865452943550, 1143241514899821, 9147521576217816, 73188119895363055

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (16,-81,146,-80).

Formula

a(0)=1, a(1)=16, a(2)=175, a(3)=1650; for n>3, a(n) = 16*a(n-1) -81*a(n-2) +146*a(n-3) -80*a(n-4). - Vincenzo Librandi, Jul 07 2013

a(0)=1, a(1)=16; for n>1, a(n) = 13*a(n-1) -40*a(n-2) +2^n -1. - Vincenzo Librandi, Jul 07 2013

a(n) = (2*8^(n+3) - 7*5^(n+3) + 14*2^(n+3) - 9)/252. [Yahia Kahloune, Jul 07 2013]

Mathematica

CoefficientList[Series[1 / ((1 - x) (1 - 2 x) (1 - 5 x) (1 -  8 x)), {x, 0, 20}], x] (* Vincenzo Librandi, Jul 07 2013 *)
LinearRecurrence[{16, -81, 146, -80}, {1, 16, 175, 1650}, 30] (* Harvey P. Dale, Nov 12 2021 *)

Prog

(Magma) I:=[1, 16, 175, 1650]; [n le 4 select I[n] else 16*Self(n-1)-81*Self(n-2)+146*Self(n-3)-80*Self(n-4): n in [1..25]]; /* or */ m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)*(1-2*x)*(1-5*x)*(1-8*x)))); // Vincenzo Librandi, Jul 07 2013

Crossrefs

Sequence in context: A215687 A187720 A017931 * A268869 A268459 A070030

Adjacent sequences: A021126 A021127 A021128 * A021130 A021131 A021132

Keyword

nonn,easy

Author

N. J. A. Sloane.

Status

approved