A021364 Expansion of 1/((1-x)(1-3x)(1-4x)(1-7x)).

1, 15, 150, 1270, 9891, 73605, 533800, 3814140, 27018981, 190442395, 1338423450, 9390536610, 65820843271, 461096642385, 3229086629100, 22609268456680, 158287591978761, 1108104188689575, 7757094081310750

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (15,-75,145,-84).

Formula

a(n) = 15*a(n-1) - 75*a(n-2) + 145*a(n-3) - 84*a(n-4), with a(0)=1, a(1)=15, a(2)=150, a(3)=1270. [Harvey P. Dale, Jun 09 2011]

a(n) = (7^(n+3) - 2*4^(n+4) + 3^(n+5) -2)/72. [Yahia Kahloune, Jun 26 2013]

a(0)=1, a(1)=15; for n>1, a(n) = 11*a(n-1) -28*a(n-2) +(3^n-1)/2. - Vincenzo Librandi, Jul 09 2013

Mathematica

CoefficientList[Series[1 / ((1 - x) (1 - 3 x) (1 - 4 x) (1 - 7 x)), {x, 0, 20}], x] (* or *) LinearRecurrence[{15, -75, 145, -84}, {1, 15, 150, 1270}, 20] (* Harvey P. Dale, Jun 09 2011 *)

Prog

(Magma) m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)*(1-3*x)*(1-4*x)*(1-7*x)))); /* or */ I:=[1, 15, 150, 1270]; [n le 4 select I[n] else 15*Self(n-1)-75*Self(n-2)+145*Self(n-3)-84*Self(n-4): n in [1..25]]; // Vincenzo Librandi, Jul 09 2013

Crossrefs

Sequence in context: A085375 A081135 A084902 * A352160 A323298 A206366

Adjacent sequences: A021361 A021362 A021363 * A021365 A021366 A021367

Keyword

nonn,easy

Author

N. J. A. Sloane.

Status

approved