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
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).
Crossrefs
Cf. A264236.
Programs
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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 *) -
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
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