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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; 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, 5,..., in the square spiral whose vertices are the triangular numbers A000217. Opposite numbers to the members of A139277 in the same spiral.
Also, sequence of numbers of the form d*A000217(n-1)+5*n with generating functions x*(5+(d-5)*x)/(1-x)^3; the inverse binomial transform is 0,5,d,0,0,.. (0 continued). See Crossrefs. - Bruno Berselli, Feb 11 2011
Even decagonal numbers divided by 2. - Omar E. Pol, Aug 19 2011
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LINKS
| O. E. Pol, Determinacion geometrica de los numeros primos y perfectos.
Index to sequences with linear recurrences with constant coefficients, signature (3,-3,1).
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FORMULA
| 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)-11 (with a(0)=0). - Vincenzo Librandi, Aug 03 2010
G.f.: x*(5+11*x)/(1-x)^3. a(n) = 4*A000217(n)+A051866(n). - Bruno Berselli, Feb 11 2011
a(n) = A028994(n)/2. - Omar E. Pol, Aug 19 2011
a(0)=0, a(1)=5, a(2)=26, a(n)=3*a(n-1)-3*a(n-2)+a(n-3) [From Harvey P. Dale, Feb 02 2012]
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EXAMPLE
| a(1)=16*1+0-11=5; a(2)=16*2+5-11=26; a(3)=16*3+26-11=63 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Aug 03 2010]
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MATHEMATICA
| 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]
Table[n(8n-3), {n, 0, 40}] (* or *) LinearRecurrence[{3, -3, 1}, {0, 5, 26}, 40] (* From Harvey P. Dale, Feb 02 2012 *)
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PROG
| (MAGMA) [ n*(8*n-3) : n in [0..40] ]; // Bruno Berselli, Feb 11 2011
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CROSSREFS
| Cf. A000217, A014634, A014635, A033585, A033586, A033587, A035008, A051870, A069129, A085250, A072279, A129272, A129274, A129275, A129276, A129278, A129279, A129280, A129281, A129282.
Cf. numbers of the form n*(d*n+10-d)/2: A008587, A056000, A028347, A140090, A014106, A028895, A045944, A186029, A007742, A022267, A033429, A022268, A049452, A186030, A135703, A152734.
Sequence in context: A083283 A049738 A042883 * A185939 A048395 A081886
Adjacent sequences: A139270 A139271 A139272 * A139274 A139275 A139276
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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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