A097334 a(n) = Sum_{k=0..n} C(n-k, floor(k/2))*2^k.

1, 3, 3, 7, 19, 31, 59, 135, 259, 495, 1035, 2071, 4051, 8191, 16475, 32679, 65443, 131343, 262059, 523831, 1049203, 2097439, 4192763, 8389575, 16779331, 33550383, 67108683, 134226007, 268427539, 536862271, 1073766299, 2147476455

Offset: 0

Author

Paul Barry, Aug 05 2004

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 (1,0,4).

Crossrefs

Cf. A089977, A097333, A097335.

Programs

Mathematica

Table[Sum[Binomial[n-k,Floor[k/2]]2^k,{k,0,n}],{n,0,40}] (* or *) LinearRecurrence[{1,0,4},{1,3,3},40] (* Harvey P. Dale, May 17 2021 *)

Formula

G.f. : (1+2x)/((1-2*x)*(1+x+2*x^2)); a(n)=a(n-1)+4a(n-3).