A021434 Expansion of 1/((1-x)(1-3x)(1-5x)(1-8x)).

1, 17, 194, 1882, 16827, 143835, 1197868, 9822164, 79783253, 644325253, 5184986742, 41632083246, 333818409679, 2674358387471, 21413929824416, 171406773741928, 1371730930238505, 10976231337133689, 87821770754328490

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,-95,199,-120).

Formula

a(n) = (8^(n+4) - 7*5^(n+4) + 14*3^(n+4) - 15)/840. - Yahia Kahloune, Jul 05 2013

a(0)=1, a(1)=17; for n>1, a(n) = 13*a(n-1) -40*a(n-2) +(3^n-1)/2. - Vincenzo Librandi, Jul 10 2013

a(0)=1, a(1)=17, a(2)=194, a(3)=1882; for n>3, a(n) = 17*a(n-1) -95*a(n-2) +199*a(n-3) -120*a(n-4). - Vincenzo Librandi, Jul 10 2013

Mathematica

CoefficientList[Series[1 / ((1 - x) (1 - 3 x) (1 - 5 x) (1 - 8 x)), {x, 0, 20}], x] (* Vincenzo Librandi, Jul 10 2013 *)
LinearRecurrence[{17, -95, 199, -120}, {1, 17, 194, 1882}, 20] (* Harvey P. Dale, Dec 10 2017 *)

Prog

(Magma) m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)*(1-3*x)*(1-5*x)*(1-8*x)))); /+ or */ I:=[1, 17, 194, 1882]; [n le 4 select I[n] else 17*Self(n-1)-95*Self(n-2)+199*Self(n-3)-120*Self(n-4): n in [1..25]]; // Vincenzo Librandi, Jul 10 2013

Crossrefs

Sequence in context: A160658 A140537 A359698 * A019316 A262111 A238672

Adjacent sequences: A021431 A021432 A021433 * A021435 A021436 A021437

Keyword

nonn,easy

Author

N. J. A. Sloane.

Status

approved