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A292296
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Sum of values of vertices of type B at level n of the hyperbolic Pascal pyramid.
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1
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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
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OFFSET
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0,4
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LINKS
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FORMULA
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a(n) = 5*a(n-1) - 6*a(n-2) + 2*a(n-3), n >= 4.
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)
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MATHEMATICA
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CoefficientList[Series[6*x^3/((1 - x)*(1 - 4*x + 2*x^2)), {x, 0, 30}],
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PROG
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(PARI) concat(vector(3), Vec(6*x^3 / ((1 - x)*(1 - 4*x + 2*x^2)) + O(x^30))) \\ Colin Barker, Sep 17 2017
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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