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Search: id:A139272
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| 0, 3, 22, 57, 108, 175, 258, 357, 472, 603, 750, 913, 1092, 1287, 1498, 1725, 1968, 2227, 2502, 2793, 3100, 3423, 3762, 4117, 4488, 4875, 5278, 5697, 6132, 6583, 7050, 7533, 8032, 8547, 9078, 9625, 10188, 10767, 11362, 11973, 12600
(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, 3,..., in the square spiral whose vertices are the triangular numbers A000217. Opposite numbers to the members of A139276 in the same spiral.
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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 - 5*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++ +3; AppendTo[lst, s], {n, 0, 7!, 16}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Nov 16 2008]
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CROSSREFS
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Cf. A000217, A014634, A014635, A033585, A033586, A033587, A035008, A051870, A069129, A085250, A072279, A129273, A129274, A129275, A129276, A129278, 129279, A129280, A129281, A129282.
Sequence in context: A079039 A041103 A104604 this_sequence A006532 A005288 A143166
Adjacent sequences: A139269 A139270 A139271 this_sequence A139273 A139274 A139275
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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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