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

1,7

Links

Table of n, a(n) for n=1..55.

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)

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 *)

Crossrefs

Sequence in context: A125681 A021899 A176435 * A204155 A363232 A355673

Adjacent sequences: A133719 A133720 A133721 * A133723 A133724 A133725

Keyword

nonn

Author

N. J. A. Sloane, Dec 30 2007

Status

approved