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A135705
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10*binomial(n,2) + 9*n.
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7
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0, 9, 28, 57, 96, 145, 204, 273, 352, 441, 540, 649, 768, 897, 1036, 1185, 1344, 1513, 1692, 1881, 2080, 2289, 2508, 2737, 2976, 3225, 3484, 3753, 4032, 4321, 4620, 4929, 5248, 5577, 5916, 6265, 6624, 6993, 7372, 7761, 8160, 8569, 8988, 9417, 9856, 10305, 10764
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Also, second 12-gonal (or dodecagonal) numbers. Identity for the numbers b(n)=n*(h*n+h-2)/2 (see Crossrefs): sum[(b(n)+i)^2, i=0..n] = sum[(b(n)+i)^2, i=n+1..2*n]+h*(h-4)*A000217(n)^2 for n>0. - Bruno Berselli, Jan 15 2011
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REFERENCES
| L. Hogben, Choice and Chance by Cardpack and Chessboard. Vol. 1, Chanticleer Press, NY, 1950, p. 36.
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LINKS
| Index to sequences with linear recurrences with constant coefficients, signature (3,-3,1).
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FORMULA
| O.g.f.: -x*(9+x)/(-1+x)^3 . a(n)=n(5n+4). - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Mar 06 2008
a(n)=a(n-1)+10*n-1 (with a(0)=0) [From Vincenzo Librandi, Nov 24 2009]
a(n)=sum[A017377(i), i=0..n-1] for n>0. - Bruno Berselli, Jan 15 2011
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MATHEMATICA
| s=0; lst={s}; Do[s+=n++ +9; AppendTo[lst, s], {n, 0, 7!, 10}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Nov 17 2008]
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CROSSREFS
| Second n-gonal numbers: A005449, A014105, A147875, A045944, A179986, A033954, A062728.
Sequence in context: A015245 A031308 A063155 * A041359 A034126 A034677
Adjacent sequences: A135702 A135703 A135704 * A135706 A135707 A135708
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Mar 04 2008
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