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 A267192 Column 3 of triangle in A059317 (the Pascal "Rhombus"). 2
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified February 26 03:53 EST 2024. Contains 370335 sequences. (Running on oeis4.)