A292296 Sum of values of vertices of type B at level n of the hyperbolic Pascal pyramid.

0, 0, 0, 6, 30, 114, 402, 1386, 4746, 16218, 55386, 189114, 645690, 2204538, 7526778, 25698042, 87738618, 299558394, 1022756346, 3491908602, 11922121722, 40704669690, 138974435322, 474488401914, 1620004737018, 5531042144250, 18884159102970, 64474552123386

Offset

0,4

Links

Colin Barker, Table of n, a(n) for n = 0..1000

László Németh, Hyperbolic Pascal pyramid, arXiv:1511.0267 [math.CO], 2015 (2nd line of Table 2).

Index entries for linear recurrences with constant coefficients, signature (5,-6,2).

Formula

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

From Colin Barker, Sep 17 2017: (Start)

G.f.: 6*x^3 / ((1 - x)*(1 - 4*x + 2*x^2)).

a(n) = (1/2)*(-12 + (9-6*sqrt(2))*(2+sqrt(2))^n + (2-sqrt(2))^n*(9+6*sqrt(2))) for n>0.

(End)

Mathematica

CoefficientList[Series[6*x^3/((1 - x)*(1 - 4*x + 2*x^2)), {x, 0, 30}],
x] (* Wesley Ivan Hurt, Sep 17 2017 *)

Prog

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

Crossrefs

Cf. A264237.

Sequence in context: A258723 A225382 A245804 * A003211 A334331 A117489

Adjacent sequences: A292293 A292294 A292295 * A292297 A292298 A292299

Keyword

nonn,easy

Author

Eric M. Schmidt, Sep 14 2017

Status

approved