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A021354 Expansion of 1/((1-x)(1-3x)(1-4x)(1-6x)). 1
1, 14, 129, 994, 6965, 46158, 295513, 1850618, 11423709, 69851782, 424437377, 2568196722, 15496267333, 93328343486, 561380193321, 3373943212906, 20266372059437, 121689277194870, 730500423652945 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

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

Index entries for linear recurrences with constant coefficients, signature (14,-67,126,-72).

FORMULA

a(0)=1, a(1)=14; for n>1, a(n) = 10*a(n-1) -24*a(n-2) +(3^n-1)/2. - Vincenzo Librandi, Jul 09 2013

a(0)=1, a(1)=14, a(2)=129, a(3)=994; for n>3, a(n) = 14*a(n-1) -67*a(n-2) +126*a(n-3) -72*a(n-4). - Vincenzo Librandi, Jul 09 2013

MATHEMATICA

CoefficientList[Series[1 / ((1 - x) (1 - 3 x) (1 - 4 x) (1 - 6 x)), {x, 0, 25}], x] (* Vincenzo Librandi, Jul 09 2013 *)

PROG

(MAGMA) m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)*(1-3*x)*(1-4*x)*(1-6*x)))); /* or */ I:=[1, 14, 129, 994]; [n le 4 select I[n] else 14*Self(n-1)-67*Self(n-2)+126*Self(n-3)-72*Self(n-4): n in [1..25]]; // Vincenzo Librandi, Jul 09 2013

CROSSREFS

Sequence in context: A222571 A038841 A240189 * A208427 A006565 A206207

Adjacent sequences:  A021351 A021352 A021353 * A021355 A021356 A021357

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified November 13 10:29 EST 2019. Contains 329093 sequences. (Running on oeis4.)