A292297 Sum of values of vertices of type C at level n of the hyperbolic Pascal pyramid.

0, 0, 0, 6, 36, 210, 1452, 12138, 114684, 1147002, 11729148, 120902202, 1249686492, 12929303130, 133809210108, 1384977143610, 14335551770268, 148385432561562, 1535924231893308, 15898233466089210, 164561459781232092, 1703363953470584922, 17631399812695032444

Offset: 0

Author

Eric M. Schmidt, Sep 14 2017

Keywords

• nonn
• easy

Links

• Colin Barker, Table of n, a(n) for n = 0..988
• László Németh, Hyperbolic Pascal pyramid, arXiv:1511.0267 [math.CO], 2015 (3rd line of Table 2).
• Index entries for linear recurrences with constant coefficients, signature (18,-99,226,-224,92,-12).

Crossrefs

Cf. A264237.

Programs

Mathematica

CoefficientList[Series[6*x^3*(1 - 12*x + 26*x^2 - 20*x^3)/((1 - x)*(1 - 4*x + 2*x^2)*(1 - 13*x + 28*x^2 - 6*x^3)), {x, 0, 20}], x] (* Wesley Ivan Hurt, Sep 17 2017 *)

PARI

concat(vector(3), Vec(6*x^3*(1 - 12*x + 26*x^2 - 20*x^3) / ((1 - x)*(1 - 4*x + 2*x^2)*(1 - 13*x + 28*x^2 - 6*x^3)) + O(x^30))) \\ Colin Barker, Sep 17 2017

Formula

a(n) = 18*a(n-1) - 99*a(n-2) + 226*a(n-3) - 224*a(n-4) + 92*a(n-5) - 12*a(n-6), n >= 7.

G.f.: 6*x^3*(1 - 12*x + 26*x^2 - 20*x^3) / ((1 - x)*(1 - 4*x + 2*x^2)*(1 - 13*x + 28*x^2 - 6*x^3)). - Colin Barker, Sep 17 2017