A021374 Expansion of 1/((1-x)(1-3x)(1-4x)(1-8x)).

1, 16, 173, 1604, 13833, 115032, 938821, 7588108, 61024865, 489508448, 3921394269, 31392726612, 251228899897, 2010181938664, 16082865641717, 128668587186716, 1029371410275729, 8235062327044080, 65880863376836365

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (16,-83,164,-96).

Formula

a(0)=1, a(1)=16; for n>1, a(n) = 12*a(n-1) -32*a(n-2) +(3^n-1)/2. - Vincenzo Librandi, Jul 09 2013

a(0)=1, a(1)=16, a(2)=173, a(3)=1604; for n>3, a(n) = 16*a(n-1) -83*a(n-2) +164*a(n-3) -96*a(n-4). - Vincenzo Librandi, Jul 09 2013

Mathematica

CoefficientList[Series[1 / ((1 - x) (1 - 3 x) (1 - 4 x) (1 - 8 x)), {x, 0, 20}], 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)*(1-8*x)))); /* or */ I:=[1, 16, 173, 1604]; [n le 4 select I[n] else 16*Self(n-1)-83*Self(n-2)+164*Self(n-3)-96*Self(n-4): n in [1..25]]; // Vincenzo Librandi, Jul 09 2013

Crossrefs

Sequence in context: A221789 A018209 A021174 * A253343 A215687 A187720

Adjacent sequences: A021371 A021372 A021373 * A021375 A021376 A021377

Keyword

nonn,easy

Author

N. J. A. Sloane.

Status

approved