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Search: id:A139278
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| 0, 15, 46, 93, 156, 235, 330, 441, 568, 711, 870, 1045, 1236, 1443, 1666, 1905, 2160, 2431, 2718, 3021, 3340, 3675, 4026, 4393, 4776, 5175, 5590, 6021, 6468, 6931, 7410, 7905, 8416, 8943, 9486, 10045, 10620, 11211, 11818, 12441, 13080
(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 segment (0, 15) together with the line from 15, in the direction 15, 46,..., 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 + 7n.
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)-17 (with a(1)=0) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Nov 13 2009]
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EXAMPLE
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For n=2, a(2)=16*2+0-17=15; n=3, a(3)=16*3+15-17=46; n=4, a(4)=16*4+46-17=93 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Nov 13 2009]
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CROSSREFS
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Cf. A000217, A014634, A014635, A033585, A033586, A033587, A035008, A051870, A069129, A085250, A072279, A129272, A129273, A129274, A129275, A129276, A129277, 129279, A129280, A129281, A129282.
Sequence in context: A033480 A041434 A136430 this_sequence A041436 A042007 A041438
Adjacent sequences: A139275 A139276 A139277 this_sequence A139279 A139280 A139281
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KEYWORD
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easy,nonn,new
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AUTHOR
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Omar E. Pol (info(AT)polprimos.com), Apr 26 2008
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