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A126274
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Partial sum of hexagonal prism numbers (A005915).
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3
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1, 15, 72, 220, 525, 1071, 1960, 3312, 5265, 7975, 11616, 16380, 22477, 30135, 39600, 51136, 65025, 81567, 101080, 123900, 150381, 180895, 215832, 255600, 300625, 351351, 408240, 471772, 542445, 620775, 707296, 802560, 907137, 1021615
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OFFSET
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0,2
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COMMENTS
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This is a 4-dimensional pyramidal number sequence whose slices are hexagonal prism numbers. A005915 Hexagonal prism numbers: (n + 1)(3n^2 + 3n + 1).
a(n) = (n+1)*A000578(n+1)-sum[i=0..n] A000578(i). [Bruno Berselli, Apr 24 2010]
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 0..1000
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FORMULA
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a(n) = sum[i=0..n] (i + 1)*(3*i^2 + 3*i + 1) = (3*n^4 + 6*n^3 + 3*n^2)/4 + 2*n^3 + 5*n^2 + 4*n + 1.
a(n) = (1/4)*(n + 1)^2(n + 2)(3 n + 2). G.f.: (1 + 10 x + 7 x^2)/(1 - x)^5. - N-E. Fahssi, May 03 2008
a(n) = sum_{i=1..n} sum_{j=1..n} sum_{k=1..n} max(i,j,k). - Enrique Pérez Herrero, Feb 26 2013
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EXAMPLE
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a(16) = 1 + 14 + 57 + 148 + 305 + 546 + 889 + 1352 + 1953 + 2710 + 3641 + 4764 + 6097 + 7658 + 9465 + 11536 + 13889 = 65025 = 3^2 * 5^2 * 17^2.
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PROG
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(MAGMA) [1/4*(n + 1)^2*(n + 2)*(3*n + 2): n in [0..30]]; // Vincenzo Librandi, May 16 2011
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CROSSREFS
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Cf. A005915.
Sequence in context: A000475 A145053 A168298 * A212097 A212098 A053531
Adjacent sequences: A126271 A126272 A126273 * A126275 A126276 A126277
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KEYWORD
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easy,nonn
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AUTHOR
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Jonathan Vos Post, Mar 09 2007
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EXTENSIONS
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Corrected and extended by Vincenzo Librandi, May 16 2011
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STATUS
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approved
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