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

0,5

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).

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

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 *)

Prog

(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

Crossrefs

Cf. A264236.

Sequence in context: A361553 A356362 A356361 * A073985 A197209 A317527

Adjacent sequences: A292290 A292291 A292292 * A292294 A292295 A292296

Keyword

nonn,easy

Author

Eric M. Schmidt, Sep 13 2017

Status

approved