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Search: id:A007585
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| A007585 |
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10-gonal (or decagonal) pyramidal numbers: n(n+1)(8n-5)/6.
(Formerly M4791)
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+0
7
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| 0, 1, 11, 38, 90, 175, 301, 476, 708, 1005, 1375, 1826, 2366, 3003, 3745, 4600, 5576, 6681, 7923, 9310, 10850, 12551, 14421, 16468, 18700, 21125, 23751, 26586, 29638, 32915, 36425, 40176, 44176, 48433, 52955, 57750
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Binomial transform of [1, 10, 17, 8, 0, 0, 0,...] = (1, 11, 38, 90,...). [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Mar 18 2009]
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
A. H. Beiler, Recreations in the Theory of Numbers, Dover, NY, 1964, p. 194.
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FORMULA
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a(n)= (8*n-5)*binomial(n+1, 2)/3. G.f.: x*(1+7*x)/(1-x)^4.
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CROSSREFS
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Cf. A001107.
Cf. A093565 ((8, 1) Pascal, column m=3). Partial sums of A001107.
Sequence in context: A139276 A010002 A143109 this_sequence A024202 A133258 A103738
Adjacent sequences: A007582 A007583 A007584 this_sequence A007586 A007587 A007588
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KEYWORD
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nonn,easy,nice
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), R. K. Guy.
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