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Search: id:A154153
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| A154153 |
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Indices k such that 28 plus the k-th triangular number is a perfect square. |
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+0
2
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| 6, 8, 47, 57, 278, 336, 1623, 1961, 9462, 11432, 55151, 66633, 321446, 388368, 1873527
(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: 28+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*(-6-2*x-3*x^2+2*x^3+7*x^4)/((x-1) * (x^2-2*x-1) * (x^2+2*x-1)) = (14+1/(x-1)+(14+29*x)/(x^2-2*x-1)+(-1-12*x)/(x^2+2*x-1))/2 .
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EXAMPLE
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6*(6+1)/2+28 = 7^2. 8*(8+1)/2+28 = 8^2. 47*(47+1)/2+28 = 34^2. 57*(57+1)/2+28 = 41^2.
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CROSSREFS
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Cf. A000217, A000290, A006451.
Sequence in context: A038262 A054102 A000380 this_sequence A164640 A167481 A137122
Adjacent sequences: A154150 A154151 A154152 this_sequence A154154 A154155 A154156
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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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