A010756 Sum along upward diagonal of Pascal triangle from (but not including) center.

0, 0, 1, 0, 1, 3, 1, 4, 11, 5, 16, 41, 22, 63, 155, 92, 247, 591, 376, 967, 2267, 1518, 3785, 8735, 6085, 14820, 33775, 24285, 58060, 130965, 96647, 227612, 509015, 383911, 892926, 1982269, 1523117, 3505386, 7732659, 6037745, 13770404, 30208749

Offset

0,6

Links

David A. Corneth, Table of n, a(n) for n = 0..4992 (terms <= 10^1000)

Maple

A010756 := proc(d)
    local a, n, m;
    a := 0 ;
    for n from 0 to d do
        m := d-n ;
        if m >= 1+floor(d/3) then
            a := a+binomial(n, m) ;
        end if;
    end do:
    a ;
end proc: # R. J. Mathar, Feb 08 2016

Mathematica

A010756[d_] := Module[{a, n, m}, a = 0; For[n = 0, n <= d, n++, m = d - n; If[m >= 1 + Floor[d/3], a = a + Binomial[n, m]]]; a]; Array[A010756, 42, 0] (* Jean-François Alcover, Dec 12 2016, after R. J. Mathar *)

Prog

(PARI) a(n) = {if(n==0, return(0)); my(u = (2*n - 1)\3); sum(i = 1, u, binomial(i, n-i)) \\ David A. Corneth, Apr 03 2021

Crossrefs

Cf. A004396.

Sequence in context: A180063 A125077 A065253 * A191857 A248044 A153278

Adjacent sequences: A010753 A010754 A010755 * A010757 A010758 A010759

Keyword

nonn

Author

R. K. Guy

Status

approved