A293636 a(1) = a(2) = 1; a(n) = ( Sum_{i|(n-1)} a(i) ) + Sum_{j|(n-2)} a(j).

1, 1, 3, 6, 12, 21, 39, 66, 114, 192, 324, 531, 888, 1452, 2382, 3891, 6363, 10329, 16833, 27303, 44349, 71907, 116625, 188859, 306114, 495615, 802632, 1299255, 2103504, 3404259, 5510376, 8917248, 14431590, 23353131, 37791414, 61150962, 98953434, 160115403, 259085673, 419218803

Offset: 1

Author

Ilya Gutkovskiy, Oct 13 2017

Keywords

• nonn

Crossrefs

Cf. A000045, A001622, A003238, A007439.

Programs

Mathematica

a[n_] := a[n] = Sum[a[i], {i, Divisors[n - 1]}] + Sum[a[j], {j, Divisors[n - 2]}]; a[1] = a[2] = 1; Table[a[n], {n, 1, 40}]

Formula

a(n) ~ c*phi^n, where phi is the golden ratio (A001622) and c = 1.83226227102725... (conjecture).