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A264851
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a(n) = n*(n + 1)*(n + 2)*(4*n - 3)/6.
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2
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0, 1, 20, 90, 260, 595, 1176, 2100, 3480, 5445, 8140, 11726, 16380, 22295, 29680, 38760, 49776, 62985, 78660, 97090, 118580, 143451, 172040, 204700, 241800, 283725, 330876, 383670, 442540, 507935, 580320, 660176, 748000, 844305, 949620, 1064490, 1189476
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OFFSET
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0,3
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COMMENTS
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Partial sums of 18-gonal (or octadecagonal) pyramidal numbers. Therefore, this is the case k=8 of the general formula n*(n + 1)*(n + 2)*(k*n - k + 2)/12, which is related to 2*(k+1)-gonal pyramidal numbers.
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LINKS
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FORMULA
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G.f.: x*(1 + 15*x)/(1 - x)^5.
a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5). - Vincenzo Librandi, Nov 27 2015
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MATHEMATICA
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Table[n (n + 1) (n + 2) (4 n - 3)/6, {n, 0, 50}]
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PROG
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(Magma) [n*(n + 1)*(n + 2)*(4*n - 3)/6: n in [0..50]]; // Vincenzo Librandi, Nov 27 2015
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CROSSREFS
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Cf. similar sequences with formula n*(n+1)*(n+2)*(k*n-k+2)/12 listed in A264850.
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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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