A021394 Expansion of 1/((1-x)(1-3x)(1-4x)(1-11x)).

1, 19, 254, 3014, 34155, 380073, 4199368, 46270588, 509296469, 5603570687, 61644604242, 678112219122, 7459321497343, 82052887210261, 902583169445276, 9928420525951016, 109212648498243177, 1201339224525513195

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (19,-107,221,-132).

Formula

a(0)=1, a(1)=19; for n>1, a(n) = 15*a(n-1) -44*a(n-2) +(3^n-1)/2. - Vincenzo Librandi, Jul 09 2013

a(0)=1, a(1)=19, a(2)=254, a(3)=3014; for n>3, a(n) = 19*a(n-1) -107*a(n-2) +221*a(n-3) -132*a(n-4). - Vincenzo Librandi, Jul 09 2013

a(n) = (3*11^(n+3) - 80*4^(n+3) + 105*3^(n+3) - 28)/1680. [Yahia Kahloune, Aug 12 2013]

Maple

A021394:=n->(3*11^(n+3) - 80*4^(n+3) + 105*3^(n+3) - 28)/1680; seq(A021394(n), n=0..100); # Wesley Ivan Hurt, Nov 11 2013

Mathematica

CoefficientList[Series[1 / ((1 - x) (1 - 3 x) (1 - 4 x) (1 - 11 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)*(1-11*x)))); /* or */ I:=[1, 19, 254, 3014]; [n le 4 select I[n] else 19*Self(n-1)-107*Self(n-2)+221*Self(n-3)-132*Self(n-4): n in [1..25]]; // Vincenzo Librandi, Jul 09 2013

Crossrefs

Sequence in context: A185425 A009728 A027532 * A016316 A021154 A255722

Adjacent sequences: A021391 A021392 A021393 * A021395 A021396 A021397

Keyword

nonn,easy

Author

N. J. A. Sloane.

Status

approved