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Search: id:A007587
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| A007587 |
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12-gonal (or dodecagonal) pyramidal numbers: n(n+1)(10n-7)/6.
(Formerly M4895)
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+0
4
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| 0, 1, 13, 46, 110, 215, 371, 588, 876, 1245, 1705, 2266, 2938, 3731, 4655, 5720, 6936, 8313, 9861, 11590, 13510, 15631, 17963, 20516, 23300, 26325, 29601, 33138, 36946, 41035, 45415, 50096, 55088, 60401, 66045
(list; graph; listen)
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OFFSET
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0,3
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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)=(10*n-7)*binomial(n+1, 2)/3. G.f.: x*(1+9*x)/(1-x)^4.
Binomial transform of [1, 12, 21, 10, 0, 0, 0,...] = (1, 13, 46, 110,...). - Gary W. Adamson (qntmpkt(AT)yahoo.com), Nov 28 2007
a(n) = Sum_{k=0..n} k*(5*k-4). [From Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Nov 20 2008]
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PROGRAM
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(MAGMA) [ n eq 1 select 0 else Self(n-1)+(n-1)*(5*n-9): n in [1..35] ]; [From Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Nov 20 2008]
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CROSSREFS
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Cf. A093645 ((10, 1) Pascal, column m=3). Partial sums of A051624.
Sequence in context: A121964 A147208 A010003 this_sequence A034462 A116476 A035340
Adjacent sequences: A007584 A007585 A007586 this_sequence A007588 A007589 A007590
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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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