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A281698
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a(n) = 5*2^(n-1) + 2^(2*n-1) + 6^n + 1.
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2
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5, 14, 55, 269, 1465, 8369, 48865, 288449, 1713025, 10210049, 60993025, 364899329, 2185181185, 13094268929, 78498422785, 470721937409, 2823257554945, 16935249707009, 101594317062145, 609497180274689, 3656708198498305, 21939149668876289, 131630499945775105
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OFFSET
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0,1
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COMMENTS
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Similar to A279511 Sierpinski square-based pyramid but with tetrahedral openings as found in the structure of the Sierpinski octahedron A279512.
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LINKS
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FORMULA
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a(n) = 13*a(n-1) - 56*a(n-2) + 92*a(n-3) - 48*a(n-4) for n>3.
G.f.: (5 - 51*x + 153*x^2 - 122*x^3) / ((1 - x)*(1 - 2*x)*(1 - 4*x)*(1 - 6*x)).
(End)
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MAPLE
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MATHEMATICA
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Table[5*2^(n - 1) + 2^(2 n - 1) + 6^n + 1, {n, 0, 22}] (* or *)
LinearRecurrence[{13, -56, 92, -48}, {5, 14, 55, 269}, 23] (* or *)
CoefficientList[Series[(5 - 51 x + 153 x^2 - 122 x^3)/((1 - x) (1 - 2 x) (1 - 4 x) (1 - 6 x)), {x, 0, 22}], x] (* Michael De Vlieger, Jan 28 2017 *)
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PROG
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(PARI) Vec((5 - 51*x + 153*x^2 - 122*x^3) / ((1 - x)*(1 - 2*x)*(1 - 4*x)*(1 - 6*x)) + O(x^30)) \\ Colin Barker, Jan 28 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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