A128610 a(0)=a(1)=1. For n >= 2, a(n) = a(n-2) + a(n-1) + (number of terms from among {a(0),a(1),a(2),...a(n-1)} which are <= n).

1, 1, 4, 7, 14, 24, 41, 69, 114, 187, 305, 496, 805, 1305, 2115, 3425, 5545, 8975, 14525, 23505, 38035, 61545, 99585, 161135, 260726, 421867, 682599, 1104472, 1787077, 2891555, 4678638, 7570199, 12248843, 19819048, 32067897, 51886951, 83954854

Offset

0,3

Links

Table of n, a(n) for n=0..36.

Example

There are 4 terms among the terms {a(0),a(1),a(2),...a(8)} which are <= 9. So a(9) = a(7) + a(8) + 4 = 69 + 114 + 4 = 187.

Maple

a[0]:=1:a[1]:=1: for n from 2 to 42 do ct:=2: for j from 2 to n-1 do if a[j]<=n then ct:=ct+1 else fi od: a[n]:=a[n-1]+a[n-2]+ct od: seq(a[n], n=0..42); # Emeric Deutsch, May 09 2007

Crossrefs

Sequence in context: A003404 A139025 A221107 * A305124 A386479 A094968

Adjacent sequences: A128607 A128608 A128609 * A128611 A128612 A128613

Keyword

nonn

Author

Leroy Quet, May 08 2007

Extensions

More terms from Emeric Deutsch, May 09 2007

Status

approved