A092809 Expansion of (1+x-x^2) / ((1-x^2)*(1-4*x^2)).

1, 1, 4, 5, 16, 21, 64, 85, 256, 341, 1024, 1365, 4096, 5461, 16384, 21845, 65536, 87381, 262144, 349525, 1048576, 1398101, 4194304, 5592405, 16777216, 22369621, 67108864, 89478485, 268435456, 357913941, 1073741824, 1431655765, 4294967296, 5726623061

Offset: 0

Author

Paul Barry, Mar 10 2004

Keywords

• easy
• nonn

Comments

Partial sums of A092808.

Apply matrix A133080 to A001045(n+1). - Paul Barry, Oct 08 2009

Links

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

Crossrefs

Cf. A001045.

Programs

PARI

Vec((1+x-x^2)/((1-x)*(1+x)*(1-2*x)*(1+2*x)) + O(x^40)) \\ Colin Barker, Sep 09 2016

PARI

a(n) = if(n%2,2,3)<Charles R Greathouse IV, Sep 09 2016

Formula

a(n) = 5*2^n/6+(-2)^n/6+(-1)^n/6-1/6.

a(2*n) = 4^n = A000302(n).

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

From Colin Barker, Sep 09 2016: (Start)

a(n) = 5*a(n-2)-4*a(n-4) for n>3.

G.f.: (1+x-x^2) / ((1-x)*(1+x)*(1-2*x)*(1+2*x))

(End)