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A071910
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a(n) = t(n)*t(n+1)*t(n+2), where t() are the triangular numbers.
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1
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0, 18, 180, 900, 3150, 8820, 21168, 45360, 89100, 163350, 283140, 468468, 745290, 1146600, 1713600, 2496960, 3558168, 4970970, 6822900, 9216900, 12273030, 16130268, 20948400, 26910000, 34222500, 43120350, 53867268, 66758580, 82123650, 100328400, 121777920
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OFFSET
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0,2
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COMMENTS
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a(n) is also the number of three-dimensional cage assemblies such that the assembly is not a cube. See also A052149 for the two-dimensional version and to A059827 for the non-exclusive version. - Alejandro Rodriguez, Oct 20 2020
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LINKS
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FORMULA
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a(n) = ((n+1)*(n+2))^3/8 - Sum_{i=1..n+1} i^3. - Jon Perry, Feb 13 2004
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PROG
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(PARI) t(n) = n*(n+1)/2;
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CROSSREFS
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Cf. A006542, (first differences of a(n) /18) A006414, (second differences of a(n) /18) A006322, (third differences of a(n) /18) A004068, (fourth differences of a(n) /18) A005891, (fifth differences of a(n) /18) A008706.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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