A108474 Expansion of 1/((1-2x)*(1+4x^2)).

1, 2, 0, 0, 16, 32, 0, 0, 256, 512, 0, 0, 4096, 8192, 0, 0, 65536, 131072, 0, 0, 1048576, 2097152, 0, 0, 16777216, 33554432, 0, 0, 268435456, 536870912, 0, 0, 4294967296, 8589934592, 0, 0, 68719476736, 137438953472, 0, 0, 1099511627776

Offset

0,2

Comments

2^n with gaps. In general, Sum_{k=0..n} Sum_{j=0..n} C(2(n-k),j)*C(2k,j)*r^j has expansion (1 - (r+1)*x)/((1 + (r+3)x + (r-1)(r+3)x^2 + (r-1)^3*x^3).

Links

Table of n, a(n) for n=0..40.

Index entries for linear recurrences with constant coefficients, signature (2,-4,8).

Formula

G.f.: 1/(1-2x+4x^2-8x^3);

a(n) = 2*a(n-1) - 4*a(n-2) + 8*a(n-3);

a(n) = Sum_{k=0..n} Sum_{j=0..n} C(2(n-k), j)*C(2k, j)*(-1)^j.

a(n) = 2^n*A133872(n). - R. J. Mathar, Mar 08 2021

Crossrefs

Sequence in context: A120560 A158465 A003193 * A120582 A003784 A368849

Adjacent sequences: A108471 A108472 A108473 * A108475 A108476 A108477

Keyword

easy,nonn

Author

Paul Barry, Jun 04 2005

Status

approved