A133722 Column 3 of triangle in A133721.

0, 0, 1, 1, 1, 1, 7, 3, 1, 25, 6, 1, 65, 10, 1, 140, 15, 1, 266, 21, 1, 462, 28, 1, 750, 36, 1, 1155, 45, 1, 1705, 55, 1, 2431, 66, 1, 3367, 78, 1, 4550, 91, 1, 6020, 105, 1, 7820, 120, 1, 9996, 136, 1, 12597, 153, 1, 15675

Offset: 1

Author

N. J. A. Sloane, Dec 30 2007

Keywords

• nonn

Programs

Maple

A133722 := proc(n)
        A133721(n,3) ;
end proc:
seq(A133722(n),n=1..60) ; # R. J. Mathar, Nov 23 2011

Mathematica

A133713[l_, cl_] := Module[{g, k, s}, g = 1; For[k = 1, k <= cl + 1, k++, s = Sum[Binomial[Binomial[l, k + 1] + i - 1, i]*t^(i*k), {i, 0, Ceiling[ cl/k]}]; g = g*s]; SeriesCoefficient[g, {t, 0, cl}]];
a[m_, n_] := A133713[Ceiling[m/n], n*Ceiling[m/n] - m];
Table[a[m, 3], {m, 1, 55}] (* Jean-François Alcover, Apr 03 2020, after R. J. Mathar *)

Formula

Conjectures from Colin Barker, Apr 03 2020: (Start)

G.f.: x^3*(1 + x + x^2 - 4*x^3 + 2*x^4 - 2*x^5 + 6*x^6 + x^8 - 4*x^9 + x^12) / ((1 - x)^5*(1 + x + x^2)^5).

a(n) = 5*a(n-3) - 10*a(n-6) + 10*a(n-9) - 5*a(n-12) + a(n-15) for n>14.

(End)