A086462 Expansion of (1+x)(1+4x)/((1-x)(1-4x)).

1, 10, 50, 210, 850, 3410, 13650, 54610, 218450, 873810, 3495250, 13981010, 55924050, 223696210, 894784850, 3579139410, 14316557650, 57266230610, 229064922450, 916259689810, 3665038759250, 14660155037010, 58640620148050

Offset: 0

Author

Paul Barry, Jul 21 2003

Keywords

• easy
• nonn

Links

• Harvey P. Dale, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (5,-4).

Crossrefs

Cf. A001045, A002450, A072197.

Programs

Mathematica

CoefficientList[Series[(1+x)(1+4x)/((1-x)(1-4x)),{x,0,30}],x] (* or *) LinearRecurrence[{5,-4},{1,10,50},30] (* Harvey P. Dale, May 27 2023 *)

PARI

a(n) = 0^n + 10*(4^n-1)/3; \\ Ruud H.G. van Tol, Oct 11 2023

Formula

a(0) = 1, a(1) = 10, a(2) = 50, a(n) = 5*a(n-1) - 4*a(n-2).

a(n) = 10*(4^n-1)/3 + 0^n = 10*A002450(n) + 0^n = 10*A001045(2*n) + 0^n.