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A292295
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Sum of values of vertices of type A at level n of the hyperbolic Pascal pyramid.
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1
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0, 0, 6, 18, 54, 174, 582, 1974, 6726, 22950, 78342, 267462, 913158, 3117702, 10644486, 36342534, 124081158, 423639558, 1446395910, 4938304518, 16860426246, 57565095942, 196539531270, 671027933190, 2291032670214, 7822074814470, 26706233917446, 91180786040838
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OFFSET
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0,3
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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^2*(1 - 2*x) / ((1 - x)*(1 - 4*x + 2*x^2)).
a(n) = (-3/2)*(-4 + (4-3*sqrt(2))*(2+sqrt(2))^n + (2-sqrt(2))^n*(4+3*sqrt(2))) for n>0.
(End)
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MATHEMATICA
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CoefficientList[Series[6*x^2*(1 - 2*x)/((1 - x)*(1 - 4*x + 2*x^2)), {x, 0, 30}], x] (* Wesley Ivan Hurt, Sep 17 2017 *)
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PROG
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(PARI) concat(vector(2), Vec(6*x^2*(1 - 2*x) / ((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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