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A154144
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Indices k such that 13 plus the k-th triangular number is a perfect square.
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1
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2, 8, 23, 53, 138, 312, 807, 1821, 4706, 10616, 27431, 61877, 159882, 360648, 931863, 2102013, 5431298, 12251432, 31655927, 71406581, 184504266, 416188056, 1075369671, 2425721757
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| a(1..4)=(2,8,23,53); a(n>4)=6*a(n-2)-a(n-4)+2. [From Ctibor O. Zizka (c.zizka(AT)email.cz), Nov 10 2009]
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LINKS
| F. T. Adams-Watters, SeqFan Discussion, Oct 2009
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FORMULA
| {k: 13+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*(-2-6*x-3*x^2+6*x^3+3*x^4)/((x-1) * (x^2-2*x-1) * (x^2+2*x-1)) = (6+(-3-2*x)/(x^2+2*x-1)+1/(x-1)+(8+19*x)/(x^2-2*x-1))/2 .
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EXAMPLE
| 2*(2+1)/2+13 = 4^2. 8*(8+1)/2+13 = 7^2. 23*(23+1)/2+13 = 17^2. 53*(53+1)/2+13 = 38^2.
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MATHEMATICA
| With[{nn=25000}, Transpose[Select[Thread[{Range[nn], Accumulate[ Range[nn]]}], IntegerQ[Sqrt[#[[2]]+13]]&]][[1]]] (* From Harvey P. Dale, Jan 13 2012 *)
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CROSSREFS
| Cf. A000217, A000290, A006451.
Sequence in context: A190021 A014285 A079460 * A180664 A018042 A072842
Adjacent sequences: A154141 A154142 A154143 * A154145 A154146 A154147
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KEYWORD
| nonn,more
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AUTHOR
| R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 18 2009
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EXTENSIONS
| a(16)-a(24) from Donovan Johnson (donovan.johnson(AT)yahoo.com), Nov 01 2010
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