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A300624
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Figurate numbers based on the 11-dimensional regular convex polytope called the 11-dimensional cross-polytope, or 11-dimensional hyperoctahedron.
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2
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0, 1, 22, 243, 1804, 10165, 46530, 180775, 614680, 1871145, 5188590, 13286043, 31760676, 71513949, 152784282, 311603535, 609802800, 1150082385, 2098144710, 3714481475, 6399123260, 10753517061, 17664712562, 28418229623, 44847366984, 69528316025, 106032285086
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OFFSET
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0,3
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COMMENTS
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The 11-dimensional cross-polytope is represented by the Schlaefli symbol {3, 3, 3, 3, 3, 3, 3, 3, 3, 4}. It is the dual of the 11-dimensional hypercube.
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (12,-66,220,-495,792,-924,792,-495,220,-66,12,-1).
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FORMULA
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a(n) = 11-crosspolytope(n).
G.f.: x*(1 + x)^10 / (1 - x)^12.
a(n) = (n*(14175 + 83754*n^2 + 50270*n^4 + 7392*n^6 + 330*n^8 + 4*n^10)) / 155925.
(End)
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PROG
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(PARI) concat(0, Vec(x*(1 + x)^10 / (1 - x)^12 + O(x^40))) \\ Colin Barker, Aug 15 2018
(PARI) a(n) = (n*(14175 + 83754*n^2 + 50270*n^4 + 7392*n^6 + 330*n^8 + 4*n^10)) / 155925 \\ Colin Barker, Aug 15 2018
(Magma) [(n*(14175 + 83754*n^2 + 50270*n^4 + 7392*n^6 + 330*n^8 + 4*n^10)) / 155925 : n in [0..40]]; // Wesley Ivan Hurt, Jul 17 2020
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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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