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Search: id:A051799
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| 1, 14, 60, 170, 385, 756, 1344, 2220, 3465, 5170, 7436, 10374, 14105, 18760, 24480, 31416, 39729, 49590, 61180, 74690, 90321, 108284, 128800, 152100, 178425, 208026, 241164, 278110, 319145, 364560, 414656, 469744, 530145, 596190
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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4-dimensional pyramidal number, composed of consecutive 3-dimensional slices; each of which is a 3-dimensional 12-gonal (or dodecagonal) pyramidal number; which in turn is composed of consecutive 2-dimensional slices 12-gonal numbers. - Jonathan Vos Post (jvospost2(AT)yahoo.com), Mar 17 2006
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REFERENCES
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A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 194-196.
Herbert John Ryser, Combinatorial Mathematics, "The Carus Mathematical Monographs", No. 14, John Wiley and Sons, 1963, pp. 1-8.
Murray R. Spiegel, Calculus of Finite Differences and Difference Equations, "Schaum's Outline Series", McGraw-Hill, 1971, pp. 10-20, 79-94.
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FORMULA
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a(n)=C(n+3, 3)*(5n+2)/2 = (n+1)(n+2)(n+3)(5n+2)/12.
G.f.: (1+9*x)/(1-x)^5.
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CROSSREFS
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Cf. A007587.
Cf. A093645 ((10, 1) Pascal, column m=4).
Cf. A007587, A051624.
Sequence in context: A062022 A100171 A063492 this_sequence A140184 A025415 A003695
Adjacent sequences: A051796 A051797 A051798 this_sequence A051800 A051801 A051802
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KEYWORD
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easy,nonn
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AUTHOR
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Barry E. Williams, Dec 11 1999
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