A267192 Column 3 of triangle in A059317 (the Pascal "Rhombus").

0, 0, 0, 1, 4, 19, 70, 261, 914, 3177, 10816, 36566, 122552, 408840, 1358032, 4497995, 14862112, 49019688, 161449208, 531152855, 1745892452, 5734722698, 18826352472, 61777432510, 202648614072, 664569581090, 2178948104572, 7143067052707, 23413795288008

Offset

0,5

Links

Alois P. Heinz, Table of n, a(n) for n = 0..1000

José L. Ramírez, The Pascal Rhombus and the Generalized Grand Motzkin Paths, arXiv:1511.04577 [math.CO], 2015.

Formula

Conjecture: +(n-2)*(n-3)*(n+3)*a(n) -n*(2*n-1)*(n-2)*a(n-1) -(n-1)*(5*n^2-10*n+18)*a(n-2) +n*(2*n-3)*(n-2)*a(n-3) +n*(n+1)*(n-5)*a(n-4)=0. - R. J. Mathar, Jul 23 2017

Maple

T:= proc(n, k) option remember; `if`(min(n, k)<0, 0,
      `if`(k=0, 1, T(n-1, k)+T(n-1, k-1)+T(n-1, k-2)+T(n-2, k-2)))
    end:
a:= n-> T(n, n-3):
seq(a(n), n=0..30);  # Alois P. Heinz, Jan 24 2016

Mathematica

T[n_, k_] := T[n, k] = If[Min[n, k]<0, 0, If[k == 0, 1, T[n-1, k] + T[n-1, k-1] + T[n-1, k-2] + T[n-2, k-2]]];
a[n_] := T[n, n-3];
Table[a[n], {n, 0, 30}] (* Jean-François Alcover, Jun 23 2017, after Alois P. Heinz *)

Crossrefs

Cf. A059317, A106050, A106053.

Sequence in context: A217324 A129019 A167247 * A219972 A284224 A268214

Adjacent sequences: A267189 A267190 A267191 * A267193 A267194 A267195

Keyword

nonn

Author

N. J. A. Sloane, Jan 22 2016

Extensions

More terms from Alois P. Heinz, Jan 24 2016

Status

approved