A298350 a(n) = a(n-1) + a(n-2) + 2 a(ceiling(n/2)), where a(0) = 1, a(1) = 1, a(2) = 1.

1, 1, 1, 4, 7, 19, 34, 67, 115, 220, 373, 661, 1102, 1897, 3133, 5260, 8623, 14323, 23386, 38455, 62587, 102364, 166273, 270841, 439318, 713953, 1157065, 1877284, 3040615, 4928419, 7979554, 12925219, 20922019, 33875884, 54826549, 88749205, 143622526

Offset: 0

Author

Clark Kimberling, Feb 10 2018

Keywords

• nonn
• easy

Comments

a(n)/a(n-1) -> (1 + sqrt(5))/2, the golden ratio (A001622), so that (a(n)) has the growth rate of the Fibonacci numbers (A000045). See A298338 for a guide to related sequences.

Links

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

Crossrefs

Cf. A001622, A000045, A298338.

Programs

Mathematica

a[0] = 1; a[1] = 1; a[2] = 1;
a[n_] := a[n] = a[n - 1] + a[n - 2] + a[Ceiling[n/2]];
Table[a[n], {n, 0, 30}]  (* A298350 *)