A021414 Expansion of 1/((1-x)(1-3x)(1-5x)(1-6x)).

1, 15, 148, 1218, 9079, 63693, 429346, 2815296, 18097717, 114645531, 718257904, 4461736734, 27532164115, 169004094729, 1033087293022, 6293858904732, 38239893731473, 231823257614487, 1402859602945900

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (15,-77,153,-90).

Formula

a(0)=1, a(1)=15, a(2)=148, a(3)=1218, a(n)=15*a(n-1)-77*a(n-2)+153*a(n-3)- 90*a(n-4). - Harvey P. Dale, Mar 31 2013

a(n) = (8*6^(n+3)-15*5^(n+3)+10*3^(n+3)-3)/120. - Yahia Kahloune, May 07 2013

a(0)=1, a(1)=15; for n>1, a(n) = 11*a(n-1) -30*a(n-2) +(3^n-1)/2. - Vincenzo Librandi, Jul 09 2013

Mathematica

CoefficientList[Series[1 / ((1 - x) (1 - 3 x) (1 - 5 x) (1 - 6 x)), {x, 0, 30}], x] (* or *) LinearRecurrence[{15, -77, 153, -90}, {1, 15, 148, 1218}, 30] (* Harvey P. Dale, Mar 31 2013 *)

Prog

(Magma) m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)*(1-3*x)*(1-5*x)*(1-6*x)))); /* or */ I:=[1, 15, 148, 1218]; [n le 4 select I[n] else 15*Self(n-1)-77*Self(n-2)+153*Self(n-3)-90*Self(n-4): n in [1..25]]; // Vincenzo Librandi, Jul 09 2013

Crossrefs

Sequence in context: A240419 A069417 A051272 * A211847 A055431 A119998

Adjacent sequences: A021411 A021412 A021413 * A021415 A021416 A021417

Keyword

nonn,easy

Author

N. J. A. Sloane.

Status

approved