A380384 a(0)=0, a(n) = 2*(a(n-1) + ceiling(n/2)) - 1 for n>0.

0, 1, 3, 9, 21, 47, 99, 205, 417, 843, 1695, 3401, 6813, 13639, 27291, 54597, 109209, 218435, 436887, 873793, 1747605, 3495231, 6990483, 13980989, 27962001, 55924027, 111848079, 223696185, 447392397, 894784823, 1789569675, 3579139381, 7158278793, 14316557619

Offset: 0

Author

Paul Curtz, Jan 23 2025

Keywords

• nonn
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (3,-1,-3,2).

Crossrefs

Cf. A081254, A109613, A250777.

Programs

Mathematica

LinearRecurrence[{3, -1, -3, 2}, {0, 1, 3, 9}, 40] (* Amiram Eldar, Jan 24 2025 *)

Formula

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

a(n) = floor(2^n*5/3) - n - 1.

a(n) = A081254(n+1) - n - 1.

a(n) = a(n-4) + A250777(n-3).