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0, 11, 38, 81, 140, 215, 306, 413, 536, 675, 830, 1001, 1188, 1391, 1610, 1845, 2096, 2363, 2646, 2945, 3260, 3591, 3938, 4301, 4680, 5075, 5486, 5913, 6356, 6815, 7290, 7781, 8288, 8811, 9350, 9905, 10476, 11063, 11666, 12285, 12920
(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, 11,..., in the square spiral whose vertices are the triangular numbers A000217. Opposite numbers to the members of A139272 in the same spiral.
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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 + 3n.
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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EXAMPLE
| a(n)=16*n+a(n-1)-5 (with a(0)=0) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Aug 03 2010]
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MAPLE
| a(1)=16*1+0-5=11; a(2)=16*2+11-5=38; a(3)=16*3+38-5=81 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Aug 03 2010]
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MATHEMATICA
| f[n_]:=n*(8*n+3); f[Range[0, 60]] (*From Vladimir Joseph Stephan Orlovsky, Feb 05 2011*)
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CROSSREFS
| Cf. A000217, A014634, A014635, A033585, A033586, A033587, A035008, A051870, A069129, A085250, A072279, A129272, A129273, A129274, A129275, A129277, A129278, 129279, A129280, A129281, A129282.
Sequence in context: A071853 A072313 A063146 * A010002 A143109 A007585
Adjacent sequences: A139273 A139274 A139275 * A139277 A139278 A139279
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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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