A023953 Expansion of 1/((1-x)(1-6x)(1-7x)(1-12x)).

1, 26, 453, 6682, 90461, 1166802, 14626501, 180228074, 2197722861, 26629669378, 321427557269, 3870666716826, 46545364947901, 559241602629554, 6715873831334757, 80625872396459338, 967761559032496781

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (26,-223,702,-504).

Formula

a(n) = (12^(n+3) - 11*7^(n+3) + 11*6^(n+3) - 1)/330. [Yahia Kahloune, Jun 29 2013]

a(0)=1, a(1)=26, a(2)=453, a(3)=6682; for n>3, a(n) = 26*a(n-1) -223*a(n-2) +702*a(n-3) -504*a(n-4). - Vincenzo Librandi, Jul 16 2013

Mathematica

CoefficientList[Series[1 / ((1 - x) (1 - 6 x) (1 - 7 x) (1 - 12 x)), {x, 0, 20}], x] (* Vincenzo Librandi, Jul 16 2013 *)

Prog

(Magma) m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)*(1-6*x)*(1-7*x)*(1-12*x)))); /* or */ I:=[1, 26, 453, 6682]; [n le 4 select I[n] else 26*Self(n-1)-223*Self(n-2)+702*Self(n-3)-504*Self(n-4): n in [1..25]]; // Vincenzo Librandi, Jul 16 2013

Crossrefs

Sequence in context: A023540 A025979 A020970 * A020968 A025955 A022725

Adjacent sequences: A023950 A023951 A023952 * A023954 A023955 A023956

Keyword

nonn,easy

Author

N. J. A. Sloane.

Status

approved