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0, 7, 30, 69, 124, 195, 282, 385, 504, 639, 790, 957, 1140, 1339, 1554, 1785, 2032, 2295, 2574, 2869, 3180, 3507, 3850, 4209, 4584, 4975, 5382, 5805, 6244, 6699, 7170, 7657, 8160, 8679, 9214, 9765, 10332, 10915, 11514, 12129, 12760
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Sequence found by reading the line from 0, in the direction 0, 7,..., in the square spiral whose vertices are the triangular numbers A000217.
Polygonal number connection: 2P_n + 5S_n where P_n is the n-th pentagonal number and S_n is the n-th square number. [From William A. Tedeschi (fynmun(AT)att.net), Sep 12 2010]
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LINKS
| O. E. Pol, Determinacion geometrica de los numeros primos y perfectos.
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FORMULA
| 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
a(n)=16*n+a(n-1)-9 (with a(0)=0) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Aug 03 2010]
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EXAMPLE
| a(1)=16*1+0-9=7; a(2)=16*2+7-9=30; a(3)=16*3+30-9=69 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Aug 03 2010]
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MATHEMATICA
| s=0; lst={s}; Do[s+=n++ +7; AppendTo[lst, s], {n, 0, 8!, 16}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Nov 16 2008]
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CROSSREFS
| Cf. A000217, A014634, A014635, A033585, A033586, A033587, A035008, A051870, A069129, A085250, A072279, A129272, A129273, A129275, A129276, A129278, 129279, A129280, A129281, A129282.
Sequence in context: A063128 A063148 A116283 * A086640 A083474 A030440
Adjacent sequences: A139271 A139272 A139273 * A139275 A139276 A139277
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KEYWORD
| easy,nonn
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AUTHOR
| Omar E. Pol (info(AT)polprimos.com), Apr 26 2008
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