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Search: id:A126274
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| 1, 15, 72, 220, 525, 1071, 1960, 3312, 5265, 7975, 11616, 16380, 22477, 30135, 39600, 51136, 65025, 81567, 101080
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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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).
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FORMULA
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a(n) = SUM[i=0..n] (i + 1)*(3*i^2 + 3*i + 1) a(n) = (3*n^4 + 6*n^3 + 3*n^2)/4 + 2*n^3 + 5*n^2 + 4*n.
a(n) = 1/4(n + 1)^2(n + 2)(3 n + 2). G.f.: (1 + 10 x + 7 x^2)/(1 - x)^5. - Nour-Eddine Fahssi (fahssin(AT)yahoo.fr), May 03 2008
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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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CROSSREFS
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Cf. A005915.
Sequence in context: A053134 A000475 A145053 this_sequence A053531 A000476 A105451
Adjacent sequences: A126271 A126272 A126273 this_sequence 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 (jvospost3(AT)gmail.com), Mar 09 2007
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