A154152 Indices k such that 26 plus the k-th triangular number is a perfect square.

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

Offset

1,1

Links

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).

Formula

{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.

Example

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.

Mathematica

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 *)

Prog

(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

Crossrefs

Cf. A000217, A000290, A006451.

Sequence in context: A197552 A052572 A079725 * A357051 A370781 A025237

Adjacent sequences: A154149 A154150 A154151 * A154153 A154154 A154155

Keyword

nonn,less,easy

Author

R. J. Mathar, Oct 18 2009

Extensions

Extended by D. S. McNeil, Dec 05 2010

Status

approved