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A062717
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Numbers n such that 6n+1 is a perfect square.
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16
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0, 4, 8, 20, 28, 48, 60, 88, 104, 140, 160, 204, 228, 280, 308, 368, 400, 468, 504, 580, 620, 704, 748, 840, 888, 988, 1040, 1148, 1204, 1320, 1380, 1504, 1568, 1700, 1768, 1908, 1980, 2128, 2204, 2360, 2440, 2604, 2688, 2860, 2948, 3128, 3220, 3408, 3504
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Sequence allows us to find X values of the equation: 6*X^3 + X^2 = Y^2. - Mohamed Bouhamida (bhmd95(AT)yahoo.fr), Nov 06 2007
Averages of the Triangular numbers which take integer values. [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Aug 05 2009]
Even terms in A186423; union of A033579 and A033580, A010052(6*a(n)+1)=1. [Reinhard Zumkeller, Feb 21 2011]
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LINKS
| Harry J. Smith, Table of n, a(n) for n=1,...,1000
Index to sequences with linear recurrences with constant coefficients, signature (1,2,-2,-1,1)
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FORMULA
| G.f.: 4*x^2*(1+x+x^2) / ( (1+x)^2*(1-x)^3 ).
a(2n)=n(6n+2), a(2n+1)=6*n^2+10n+4. - Mohamed Bouhamida (bhmd95(AT)yahoo.fr), Nov 06 2007
a(n) = n^2+n+2*ceiling(n/2)^2 [From Gary Detlefs (gdetlefs(AT)aol.com), Feb 23 2010]
a(n) = (6*n*(n-1)+(2*n-1)*(-1)^n+1)/4. 6*a(n)+1 = A007310(n)^2. - Bruno Berselli, Nov 28 2010
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MAPLE
| seq(n^2+n+2*ceil(n/2)^2, n=0..48); [From Gary Detlefs (gdetlefs(AT)aol.com), Feb 23 2010]
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MATHEMATICA
| a=b=0; lst={}; Do[b=(a+=n*(n-1)/2)/n; If[b==IntegerPart[b], AppendTo[lst, b]], {n, 6!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Aug 05 2009]
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PROG
| (PARI) je=[]; for(n=0, 7000, if(issquare(6*n+1), je=concat(je, n))); je
(PARI) { n=0; for (m=0, 10^9, if (issquare(6*m + 1), write("b062717.txt", n++, " ", m); if (n==1000, break)) ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Aug 09 2009]
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CROSSREFS
| Equals 4 * A001318.
Cf. A005563, A046092, A001082, A002378, A036666.
Cf. A160757, A000217 [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Aug 05 2009]
Cf. A007310.
Sequence in context: A087254 A160726 A191483 * A084922 A180794 A047185
Adjacent sequences: A062714 A062715 A062716 * A062718 A062719 A062720
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KEYWORD
| easy,nonn
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AUTHOR
| Jason Earls (zevi_35711(AT)yahoo.com), Jul 14 2001
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