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A154154
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Indices n such that 30 plus the n-th triangular number is a perfect square.
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1
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3, 13, 34, 84, 203, 493, 1186, 2876, 6915, 16765, 40306, 97716, 234923, 569533, 1369234, 3319484, 7980483, 19347373, 46513666
(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: 30+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*(-3-10*x-3*x^2+10*x^3+4*x^4)/((x-1) * (x^2-2*x-1) * (x^2+2*x-1)) = (8+(-5-2*x)/(x^2+2*x-1)+(12+29*x)/(x^2-2*x-1)+1/(x-1))/2 .
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EXAMPLE
| 3*(3+1)/2+30 = 6^2. 13*(13+1)/2+30 = 11^2. 34*(34+1)/2+30 = 25^2. 84*(84+1)/2+30 = 60^2.
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PROG
| (PARI) {for (n=0, 10^9, if ( issquare(n*(n+1)\2 + 30), print1(n, ", ") ) ); }
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CROSSREFS
| Cf. A000217, A000290, A006451.
Sequence in context: A033943 A026084 A016061 * A137976 A095661 A058214
Adjacent sequences: A154151 A154152 A154153 * A154155 A154156 A154157
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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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