A298401 a(n) = a(n-1) + a(n-2) - n*a(floor(n/2)), where a(0) = 1, a(1) = 2, a(2) = 3.

1, 2, 3, -1, -10, -26, -30, -49, 1, 42, 303, 631, 1294, 2315, 4295, 7345, 11624, 18952, 29820, 47974, 71734, 113345, 171197, 270029, 410170, 647849, 997829, 1583173, 2460742, 3919360, 6159752, 9851417, 15639201, 25107026, 40101859, 64545565, 103573904

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, A298400.

Programs

Mathematica

a[0] = 1; a[1] = 2; a[2] = 3;
a[n_] := a[n] = a[n - 1] + a[n - 2] - n*a[Floor[n/2]];
Table[a[n], {n, 0, 30}]  (* A298401 *)