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Search: id:A139275
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| 0, 9, 34, 75, 132, 205, 294, 399, 520, 657, 810, 979, 1164, 1365, 1582, 1815, 2064, 2329, 2610, 2907, 3220, 3549, 3894, 4255, 4632, 5025, 5434, 5859, 6300, 6757, 7230, 7719, 8224, 8745, 9282, 9835, 10404, 10989, 11590, 12207, 12840
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Sequence found by reading the line from 0, in the direction 0, 9,..., in the square spiral whose vertices are the triangular numbers A000217.
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LINKS
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O. E. Pol, Determinacion geometrica de los numeros primos y perfectos.
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FORMULA
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a(n) = 8*n^2 + n.
Sequences of the form a(n)=8*n^2+c*n have generating functions x{c+8+(8-c)x} / (1-x)^3 and recurrence a(n)= 3a(n-1)-3a(n-2)+a(n-3). The inverse binomial transform is 0, c+8, 16, 0, 0, ... (0 continued). This applies to A139271 - A139278, positive or negative c. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), May 12 2008
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MATHEMATICA
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s=0; lst={s}; Do[s+=n++ +9; AppendTo[lst, s], {n, 0, 8!, 16}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Nov 17 2008]
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CROSSREFS
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Cf. A000217, A014634, A014635, A033585, A033586, A033587, A035008, A051870, A069129, A085250, A072279, A129272, A129273, A129274, A129276, A129278, 129279, A129280, A129281, A129282.
Sequence in context: A044086 A044467 A020163 this_sequence A133547 A100179 A106598
Adjacent sequences: A139272 A139273 A139274 this_sequence A139276 A139277 A139278
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KEYWORD
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easy,nonn
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AUTHOR
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Omar E. Pol (info(AT)polprimos.com), Apr 26 2008
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