A261368 Number of sequences F such that F(k) = F(k-1) + F(k-2), F(1), F(2) are positive integers, and there exists some integer x>2 such that F(x) = n.

0, 1, 3, 4, 7, 7, 10, 12, 13, 14, 18, 17, 22, 22, 23, 25, 28, 29, 31, 32, 36, 35, 40, 38, 41, 44, 44, 47, 51, 48, 53, 53, 56, 59, 59, 60, 64, 65, 66, 66, 71, 71, 74, 75, 77, 78, 83, 81, 84, 86, 87, 88, 94, 91, 97, 96, 97, 101, 102, 103, 107, 106, 110, 109, 112

Offset

1,3

Comments

This is the number of Fibonacci-style sequences seeded with positive integers that contain each n, after the seeds.

Links

Giovanni Resta, Table of n, a(n) for n = 1..10000

Example

For n=4, a(4) = 4 as the sequences <1,3,4,7...>, <2,1,3,4...>, <2,2,4,6...>, and <3,1,4,5...> each contain 4 outside of the initial 2 numbers.

Mathematica

a[n_] := Sum[Block[{s, L={x, y}}, While[(s = Total@L ) < n, L = Rest@ Append[L, s]]; If[s == n, 1, 0]], {x, n-1}, {y, n-x}]; Array[a, 65] (* Giovanni Resta, Aug 17 2015 *)

Prog

(PARI) isok(x, y, n) = {ny = 0; while (ny <= n, ny = x + y; if (ny == n, return (1)); x = y; y = ny; ); return (0); }
a(n) = {nb = 0; for (j=1, n-1, for (k=1, n-j, if (isok(j, k, n), nb++); ); ); nb; } \\ Michel Marcus, Aug 17 2015

Crossrefs

Sequence in context: A024605 A215630 A168563 * A307743 A257007 A070324

Adjacent sequences: A261365 A261366 A261367 * A261369 A261370 A261371

Keyword

nonn

Author

Ben Johnsrude, Aug 16 2015

Extensions

More terms from Michel Marcus, Aug 17 2015

Status

approved