A010754 Sum along upward diagonal of Pascal triangle to halfway point.

1, 1, 1, 1, 4, 5, 6, 7, 23, 30, 38, 47, 141, 188, 245, 313, 888, 1201, 1594, 2080, 5676, 7756, 10429, 13817, 36622, 50439, 68497, 91804, 237821, 329625, 451166, 610247, 1551727, 2161974, 2978230, 4058629, 10161409, 14220038, 19694622, 27007760, 66732392

Offset

0,5

Links

Seiichi Manyama, Table of n, a(n) for n = 0..1000

Formula

a(n) = Sum_{k=0..floor(n/4)} binomial(n - k, k). - Sean A. Irvine, Jun 08 2018

Mathematica

Table[Sum[Binomial[n-k, k], {k, 0, Floor[n/4]}], {n, 0, 40}] (* Vincenzo Librandi, Sep 25 2025 *)

Prog

(Magma) [&+[Binomial(n-k, k): k in [0..Floor(n/4)]]: n in [0..40]]; // Vincenzo Librandi, Sep 25 2025

Crossrefs

Cf. A000045, A007318.

Sequence in context: A030667 A030677 A071177 * A187807 A051036 A387345

Adjacent sequences: A010751 A010752 A010753 * A010755 A010756 A010757

Keyword

nonn

Author

R. K. Guy

Status

approved