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

0,4

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).

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

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 *)

Prog

(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

Crossrefs

Cf. A264237.

Sequence in context: A358539 A105492 A052748 * A353344 A353118 A357027

Adjacent sequences: A292294 A292295 A292296 * A292298 A292299 A292300

Keyword

nonn,easy

Author

Eric M. Schmidt, Sep 14 2017

Status

approved