A201865 Expansion of 1/((1-3*x)*(1+7*x)).

1, -4, 37, -232, 1705, -11692, 82573, -575824, 4037329, -28241620, 197750389, -1384075576, 9689060473, -67821828988, 474757585885, -3323288752288, 23263064312737, -162841321048996, 1139889634763461, -7979226281082760, 55854587454363721, -390982101720192844

Offset: 0

Author

Bruno Berselli, Dec 07 2011

Keywords

• sign
• easy

Links

• Bruno Berselli, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (-4,21).

Crossrefs

Cf. A014986, A083296, A083300.

Programs

Magma

m:=22; R:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-3*x)*(1+7*x))));

Mathematica

CoefficientList[Series[1/((1-3*x)*(1+7*x)), {x, 0, 22}], x]

Maxima

makelist(coeff(taylor(1/((1-3*x)*(1+7*x)), x, 0, n), x, n), n, 0, 21);

PARI

Vec(1/((1-3*x)*(1+7*x))+O(x^22))

Formula

G.f.: 1/((1-3*x)*(1+7*x)).

a(n) = (3^(n+1)+7*(-7)^n)/10.

a(n) = -4*a(n-1)+21*a(n-2) with n>0, a(-1)=0, a(0)=1.

a(n)-a(n-1) = A083300(n)*(-1)^n.

a(n)+5*a(n-1) = A083296(n) with a(-1)=0.