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Search: id:A154152
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| A154152 |
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Indices k such that 26 plus the k-th triangular number is a perfect square. |
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+0
2
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| 4, 10, 37, 67, 220, 394, 1285, 2299, 7492, 13402, 43669, 78115, 254524, 455290, 1483477
(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: 26+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*(-4-6*x-3*x^2+6*x^3+5*x^4)/((x-1) * (x^2-2*x-1) * (x^2+2*x-1)) = (10+(-3-6*x)/(x^2+2*x-1)+1/(x-1)+(12+27*x)/(x^2-2*x-1))/2 .
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EXAMPLE
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4*(4+1)/2+26 = 6^2. 10*(10+1)/2+26 = 9^2. 37*(37+1)/2+26 = 27^2. 67*(67+1)/2+26 = 48^2.
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CROSSREFS
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Cf. A000217, A000290, A006451.
Sequence in context: A149186 A052572 A079725 this_sequence A025237 A149188 A149189
Adjacent sequences: A154149 A154150 A154151 this_sequence A154153 A154154 A154155
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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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