A200864 Expansion of 1/((1+x)*(1-3*x)*(1-5*x)).

1, 7, 42, 230, 1211, 6237, 31732, 160300, 806421, 4046867, 20278622, 101525970, 508028431, 2541337897, 12710276712, 63562145240, 317843011241, 1589311911327, 7946850122002, 39735122306110, 198678226618851, 993398978359157, 4967018427590492, 24835162745336580

Offset: 0

Author

Bruno Berselli, Nov 23 2011

Keywords

• nonn
• easy

Links

• Bruno Berselli, Table of n, a(n) for n = 0..1000.
• Index entries for linear recurrences with constant coefficients, signature (7,-7,-15).

Crossrefs

Cf. A016209, A200859.

Programs

Magma

m:=24; R:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1+x)*(1-3*x)*(1-5*x))));

Mathematica

CoefficientList[Series[1/((1+x)(1-3x)(1-5x)), {x, 0, 24}], x]
LinearRecurrence[{7,-7,-15},{1,7,42},30] (* Harvey P. Dale, May 26 2015 *)

Maxima

makelist(coeff(taylor(1/((1+x)*(1-3*x)*(1-5*x)), x, 0, n), x, n), n, 0, 23);

PARI

Vec(1/((1+x)*(1-3*x)*(1-5*x))+O(x^24))

Formula

G.f.: 1/((1+x)*(1-3*x)*(1-5*x)).

a(n) = (50*5^n-27*3^n+(-1)^n)/24.

a(n) = 2*a(n-1)+3*a(n-2)+5^n for n>1, a(0)=1, a(1)=7.

a(n) = 7*a(n-1)-7*a(n-2)-15*a(n-3) for n>2, a(0)=1, a(1)=7, a(2)=42.

a(n+1)+a(n) = A005059(n+2).

a(n+2)-a(n) = A081625(n+2).