A021494 Expansion of 1/((1-x)(1-3x)(1-6x)(1-7x)).

1, 17, 192, 1822, 15743, 128499, 1010374, 7741184, 58209525, 431623621, 3166395596, 23035216386, 166469995147, 1196633240183, 8564499500658, 61079918944228, 434330031817409, 3080934011678985, 21810281396626360

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (17,-97,207,-126).

Formula

a(n) = (5*7^(n+3) - 8*6^(n+3) + 5*3^(n+3) - 2)/120. [Yahia Kahloune, Jul 05 2013]

a(0)=1, a(1)=17; for n>1, a(n) = 13*a(n-1) -42*a(n-2) +(3^n -1)/2. - Vincenzo Librandi, Jul 10 2013

a(0)=1, a(1)=17, a(2)=192, a(3)=1822; for n>3, a(n) = 17*a(n-1) -97*a(n-2) +207*a(n-3) -126*a(n-4). - Vincenzo Librandi, Jul 10 2013

Mathematica

CoefficientList[Series[1 / ((1 - x) (1 - 3 x) (1 - 6 x) (1 - 7 x)), {x, 0, 20}], x] (* Vincenzo Librandi, Jul 10 2013 *)

Prog

(Magma) m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)*(1-3*x)*(1-6*x)*(1-7*x)))); /* or */ I:=[1, 17, 192, 1822]; [n le 4 select I[n] else 17*Self(n-1)-97*Self(n-2)+207*Self(n-3)-126*Self(n-4): n in [1..25]]; // Vincenzo Librandi, Jul 10 2013

Crossrefs

Sequence in context: A025467 A322122 A210340 * A300172 A160658 A140537

Adjacent sequences: A021491 A021492 A021493 * A021495 A021496 A021497

Keyword

nonn,easy

Author

N. J. A. Sloane.

Status

approved