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A154149 Indices k such that 22 plus the k-th triangular number is a perfect square. 2
2, 12, 27, 77, 162, 452, 947, 2637, 5522, 15372, 32187, 89597, 187602, 522212, 1093427, 3043677, 6372962, 17739852, 37144347, 103395437, 216493122, 602632772, 1261814387, 3512401197, 7354393202, 20471774412, 42864544827, 119318245277, 249832875762 (list; graph; refs; listen; history; text; internal format)
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: 22+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*(-2-10*x-3*x^2+10*x^3+3*x^4)/((x-1) * (x^2-2*x-1) * (x^2+2*x-1)).

G.f.: ( 6 + (10+25*x)/(x^2-2*x-1) - 5/(x^2+2*x-1) + 1/(x-1) )/2.

EXAMPLE

2*(2+1)/2+22 = 5^2. 12*(12+1)/2+22 = 10^2. 27*(27+1)/2+22 = 20^2. 77*(77+1)/2+22 = 55^2.

MATHEMATICA

Join[{2, 12}, Select[Range[0, 10^5], ( Ceiling[Sqrt[#*(# + 1)/2]] )^2 - #*(# + 1)/2 == 22 &]] (* or *) LinearRecurrence[{1, 6, -6, -1, 1}, {2, 12, 27, 77, 162}, 25] (* G. C. Greubel, Sep 03 2016 *)

PROG

(PARI) Vec(x*(-2-10*x-3*x^2+10*x^3+3*x^4)/((x-1)*(x^2-2*x-1)*(x^2+2*x-1)) + O(x^30)) \\ Colin Barker, Jul 11 2015

CROSSREFS

Cf. A000217, A000290, A006451.

Sequence in context: A294170 A102960 A166151 * A119201 A164876 A225291

Adjacent sequences:  A154146 A154147 A154148 * A154150 A154151 A154152

KEYWORD

nonn,less,easy

AUTHOR

R. J. Mathar, Oct 18 2009

EXTENSIONS

Extended by D. S. McNeil, Dec 04 2010

STATUS

approved

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Last modified March 19 00:02 EDT 2019. Contains 321305 sequences. (Running on oeis4.)