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A100175
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Structured triakis tetrahedral numbers (vertex structure 4).
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7
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1, 8, 30, 76, 155, 276, 448, 680, 981, 1360, 1826, 2388, 3055, 3836, 4740, 5776, 6953, 8280, 9766, 11420, 13251, 15268, 17480, 19896, 22525, 25376, 28458, 31780, 35351, 39180, 43276, 47648, 52305, 57256, 62510, 68076, 73963, 80180, 86736, 93640, 100901, 108528
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OFFSET
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1,2
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COMMENTS
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Equals binomial transform of [1, 7, 15, 9, 0, 0, 0, ...] where (1, 7, 15, 9) = row 3 of triangle A038763. - Gary W. Adamson, Jul 19 2008
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LINKS
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FORMULA
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a(n) = (3*n^3 - 3*n^2 + 2*n)/2.
G.f.: x*(2*x+1)^2 / ( (x-1)^4 ).
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MATHEMATICA
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CoefficientList[Series[x (2x+1)^2/((x-1)^4), {x, 0, 50}], x] (* or *) LinearRecurrence[{4, -6, 4, -1}, {0, 1, 8, 30}, 50] (* Harvey P. Dale, Mar 18 2023 *)
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PROG
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CROSSREFS
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Cf. A000578 (alternate vertex), A100145 for more on structured numbers.
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KEYWORD
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easy,nonn
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AUTHOR
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James A. Record (james.record(AT)gmail.com), Nov 07 2004
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STATUS
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approved
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