A298400 a(n) = a(n-1) + a(n-2) - n*a(floor(n/2)), where a(0) = 1, a(1) = 1, a(2) = 1.

1, 1, 1, -1, -4, -10, -8, -11, 13, 38, 151, 299, 546, 949, 1649, 2763, 4204, 6746, 10266, 16290, 23536, 36655, 53613, 83391, 123900, 193641, 292867, 460885, 707580, 1120644, 1745334, 2780325, 4391131, 7032724, 11194491, 17991105, 28816020, 46427283, 74624283

Offset: 0

Author

Clark Kimberling, Feb 10 2018

Keywords

• easy
• sign

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, A298401.

Programs

Mathematica

a[0] = 1; a[1] = 1; a[2] = 1; a[n_] := a[n] = a[n - 1] + a[n - 2] - n*a[Floor[n/2]];
Table[a[n], {n, 0, 30}]  (* A298400 *)