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Search: id:A139273
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| 0, 5, 26, 63, 116, 185, 270, 371, 488, 621, 770, 935, 1116, 1313, 1526, 1755, 2000, 2261, 2538, 2831, 3140, 3465, 3806, 4163, 4536, 4925, 5330, 5751, 6188, 6641, 7110, 7595, 8096, 8613, 9146, 9695, 10260, 10841, 11438, 12051, 12680
(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, 5,..., in the square spiral whose vertices are the triangular numbers A000217. Opposite numbers to the members of A139277 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 - 3*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)-27 (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+0-27=5; n=3, a(3)=16*3+5-27=26; n=4, a(4)=16*4+26-27=63 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Nov 13 2009]
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MATHEMATICA
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s=0; lst={s}; Do[s+=n++ +5; 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, A129272, A129274, A129275, A129276, A129278, 129279, A129280, A129281, A129282.
Sequence in context: A083283 A049738 A042883 this_sequence A048395 A081886 A081530
Adjacent sequences: A139270 A139271 A139272 this_sequence A139274 A139275 A139276
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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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