A292293 Number of vertices of type D at level n of the hyperbolic Pascal pyramid.

0, 0, 0, 0, 3, 24, 177, 1347, 10467, 82029, 644808, 5073915, 39939900, 314427960, 2475438408, 19488960504, 153435934587, 1207997701872, 9510543548457, 74876345104299, 589500202673403, 4641125238026805, 36539501601385200, 287674887310843395, 2264859596198883588

Offset: 0

Author

Eric M. Schmidt, Sep 13 2017

Keywords

• nonn
• easy

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• László Németh, Hyperbolic Pascal pyramid, arXiv:1511.0267 [math.CO], 2015 (4th line of Table 1).
• Index entries for linear recurrences with constant coefficients, signature (12,-37,37,-12,1).

Crossrefs

Cf. A264236.

Programs

Mathematica

CoefficientList[Series[3*x^4*(1 - 4*x)/((1 - x)*(1 - 8*x + x^2)*(1 - 3*x + x^2)), {x, 0, 30}], x] (* Wesley Ivan Hurt, Sep 17 2017 *)

PARI

concat(vector(4), Vec(3*x^4*(1 - 4*x) / ((1 - x)*(1 - 8*x + x^2)*(1 - 3*x + x^2)) + O(x^30))) \\ Colin Barker, Sep 17 2017

Formula

a(n) = 12*a(n-1) - 37*a(n-2) + 37*a(n-3) - 12*a(n-4) + a(n-5), n >= 6.

G.f.: 3*x^4*(1 - 4*x) / ((1 - x)*(1 - 8*x + x^2)*(1 - 3*x + x^2)). - Colin Barker, Sep 17 2017