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A292293
Number of vertices of type D at level n of the hyperbolic Pascal pyramid.
1
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
László Németh, Hyperbolic Pascal pyramid, arXiv:1511.0267 [math.CO], 2015 (4th line of Table 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
KEYWORD
nonn,easy
AUTHOR
Eric M. Schmidt, Sep 13 2017
STATUS
approved