A298412 a(n) = 2*a(n-1) + a(n-2) + a([n/2]), where a(0) = 1, a(1) = 1, a(2) = 1.

1, 1, 1, 4, 10, 25, 64, 157, 388, 943, 2299, 5566, 13495, 32620, 78892, 190561, 460402, 1111753, 2684851, 6482398, 15651946, 37788589, 91234690, 220263535, 531775255, 1283827540, 3099462955, 7482786070, 18065113987, 43613092936, 105291490420, 254196264337

Offset: 0

Author

Clark Kimberling, Feb 11 2018

Keywords

• nonn
• easy

Comments

a(n)/a(n-1) -> 1 + sqrt(2).

Links

• Clark Kimberling, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A298338.

Programs

Mathematica

a[0] = 1; a[1] = 1; a[2] = 1;
a[n_] := a[n] = 2 a[n - 1] + a[n - 2] + a[Floor[n/2]];
Table[a[n], {n, 0, 30}]  (* A298412 *)