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Search: id:A154154
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| A154154 |
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Indices k such that 30 plus the k-th triangular number is a perfect square. |
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+0
2
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| 3, 13, 34, 84, 203, 493, 1186, 2876, 6915, 16765, 40306, 97716, 234923, 569533, 1369234
(list; graph; listen)
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OFFSET
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1,1
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LINKS
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F. T. Adams-Watters, SeqFan Discussion, Oct 2009
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FORMULA
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{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
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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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CROSSREFS
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Cf. A000217, A000290, A006451.
Sequence in context: A033943 A026084 A016061 this_sequence A137976 A095661 A058214
Adjacent sequences: A154151 A154152 A154153 this_sequence A154155 A154156 A154157
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KEYWORD
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nonn,less,more
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AUTHOR
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R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 18 2009
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