A021474 Expansion of 1/((1-x)(1-3x)(1-5x)(1-11x)).

1, 20, 278, 3388, 39039, 438648, 4872316, 53834696, 593387597, 6533322796, 71896935474, 791018479524, 8701965018475, 95725426313264, 1052998752170552, 11583081609022672, 127414374439552473

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,-122,268,-165).

Formula

a(0)=1, a(1)=20; for n>1, a(n) = 16*a(n-1) -55*a(n-2) +(3^n-1)/2. - Vincenzo Librandi, Jul 10 2013

a(0)=1, a(1)=20, a(2)=278, a(3)=3388; for n>3, a(n) = 20*a(n-1) -122*a(n-2) +268*a(n-3) -165*a(n-4). - Vincenzo Librandi, Jul 10 2013

a(n) = (11^(n+3) - 10*5^(n+3) + 15*3^(n+3) - 6)/480. [Yahia Kahloune, Sep 16 2013]

Mathematica

CoefficientList[Series[1/((1-x)(1-3x)(1-5x)(1-11x)), {x, 0, 20}], x]  (* Harvey P. Dale, Apr 02 2011 *)

Prog

(Magma) m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)*(1-3*x)*(1-5*x)*(1-11*x)))); /* or */ I:=[1, 20, 278, 3388]; [n le 4 select I[n] else 20*Self(n-1)-122*Self(n-2)+268*Self(n-3)-165*Self(n-4): n in [1..25]]; // Vincenzo Librandi, Jul 10 2013

Crossrefs

Cf. A028000.

Sequence in context: A019483 A018056 A021234 * A017999 A244653 A012836

Adjacent sequences: A021471 A021472 A021473 * A021475 A021476 A021477

Keyword

nonn,easy

Author

N. J. A. Sloane.

Status

approved