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A154148
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Indices n such that 21 plus the n-th triangular number is a perfect square.
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2
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5, 7, 40, 50, 237, 295, 1384, 1722, 8069, 10039, 47032, 58514, 274125, 341047, 1597720, 1987770, 9312197, 11585575, 54275464, 67525682
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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LINKS
| F. T. Adams-Watters, SeqFan Discussion, Oct 2009
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FORMULA
| {k: 21+k*(k+1)/2 in A000290}
Conjecture: a(n)= +a(n-1) +6*a(n-2) -6*a(n-3) -a(n-4) +a(n-5)
Conjecture: G.f.: x*(-5-2*x-3*x^2+2*x^3+6*x^4)/((x-1) * (x^2-2*x-1) * (x^2+2*x-1)) = (12+(12+25*x)/(x^2-2*x-1)+1/(x-1)+(-1-10*x)/(x^2+2*x-1))/2 .
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EXAMPLE
| 5*(5+1)/2+21 = 6^2. 7*(7+1)/2+21 = 7^2. 40*(40+1)/2+21 = 29^2. 50*(50+1)/2+21 = 36^2.
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PROG
| (PARI) {for (n=0, 10^9, if ( issquare(n*(n+1)\2 + 21), print1(n, ", ") ) ); }
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CROSSREFS
| Cf. A000217, A000290, A006451.
Sequence in context: A006067 A178428 A147760 * A153376 A189241 A167205
Adjacent sequences: A154145 A154146 A154147 * A154149 A154150 A154151
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KEYWORD
| nonn,less
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AUTHOR
| R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 18 2009
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