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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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2
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4, 10, 37, 67, 220, 394, 1285, 2299, 7492, 13402, 43669, 78115, 254524, 455290, 1483477, 2653627, 8646340, 15466474, 50394565, 90145219, 293721052, 525404842, 1711931749, 3062283835, 9977869444, 17848298170, 58155284917, 104027505187, 338953840060
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OFFSET
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1,1
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LINKS
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Colin Barker, Table of n, a(n) for n = 1..500
F. T. Adams-Watters, SeqFan Discussion, Oct 2009
Index entries for linear recurrences with constant coefficients, signature (1,6,-6,-1,1).
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FORMULA
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{k: 26+k*(k+1)/2 in A000290}.
a(n) = +a(n-1) +6*a(n-2) -6*a(n-3) -a(n-4) +a(n-5).
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)).
G.f.: ( 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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MATHEMATICA
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Join[{4, 10}, Select[Range[0, 10^5], ( Ceiling[Sqrt[#*(# + 1)/2]] )^2 - #*(# + 1)/2 == 26 &]] (* or *) LinearRecurrence[{1, 6, -6, -1, 1}, {4, 10, 37, 67, 220}, 25] (* G. C. Greubel, Sep 03 2016 *)
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PROG
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(PARI) Vec(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)) + O(x^40)) \\ Colin Barker, Jul 11 2015
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CROSSREFS
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Cf. A000217, A000290, A006451.
Sequence in context: A197552 A052572 A079725 * A025237 A149188 A149189
Adjacent sequences: A154149 A154150 A154151 * A154153 A154154 A154155
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KEYWORD
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nonn,less,easy
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AUTHOR
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R. J. Mathar, Oct 18 2009
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EXTENSIONS
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Extended by D. S. McNeil, Dec 05 2010
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STATUS
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approved
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