A292292 Number of vertices of type C at level n of the hyperbolic Pascal pyramid.

0, 0, 0, 1, 3, 9, 34, 174, 1128, 8251, 63315, 494175, 3879370, 30512736, 240149088, 1890487729, 14883249459, 117174190329, 922506823618, 7262871367566, 57180440473320, 450180590519275, 3544264121625315, 27903931958216271, 219687190433359498

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 (3rd 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.: x^3*(1 - 9*x + 10*x^2) / ((1 - x)*(1 - 8*x + x^2)*(1 - 3*x + x^2)). - Colin Barker, Sep 17 2017

a(n) = A001091(n-3)/15 + 3*A002878(n-3)/5 + 1/3 for n > 0. - Ehren Metcalfe, Apr 18 2019

Mathematica

CoefficientList[Series[x^3*(1 - 9*x + 10*x^2)/((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(3), Vec(x^3*(1 - 9*x + 10*x^2) / ((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: A219663 A084756 A009578 * A067787 A332370 A130491

Adjacent sequences: A292289 A292290 A292291 * A292293 A292294 A292295

Keyword

nonn,easy

Author

Eric M. Schmidt, Sep 13 2017

Status

approved