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A154150 Indices n such that 24 plus the n-th triangular number is a perfect square. 1
1, 15, 24, 94, 145, 551, 848, 3214, 4945, 18735, 28824, 109198, 168001, 636455, 979184, 3709534, 5707105, 21620751, 33263448, 126014974 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..20.

F. T. Adams-Watters, SeqFan Discussion, Oct 2009

FORMULA

{k: 24+k*(k+1)/2 in A000290}.

Conjectures: (Start)

a(n) = +a(n-1) +6*a(n-2) -6*a(n-3) -a(n-4) +a(n-5).

G.f.: x*(-1-14*x-3*x^2+14*x^3+2*x^4)/((x-1) * (x^2-2*x-1) * (x^2+2*x-1)).

G.f.: ( 4 + 1/(x-1) + (10+27*x)/(x^2-2*x-1) + (-7+4*x)/(x^2+2*x-1) )/2. (End)

EXAMPLE

1*(1+1)/2+24 = 5^2. 15*(15+1)/2+24 = 12^2. 24*(24+1)/2+24 = 18^2. 94*(94+1)/2+24 = 67^2.

MATHEMATICA

Join[{1, 15}, Select[Range[0, 10^5], ( Ceiling[Sqrt[#*(# + 1)/2]] )^2 - #*(# + 1)/2 == 24 &]] (* G. C. Greubel, Sep 03 2016 *)

PROG

(PARI) {for (n=0, 10^9, if ( issquare(n*(n+1)\2 + 24), print1(n, ", ") ) ); }

CROSSREFS

Cf. A000217, A000290, A006451.

Sequence in context: A162964 A067343 A247315 * A324484 A167709 A167353

Adjacent sequences:  A154147 A154148 A154149 * A154151 A154152 A154153

KEYWORD

nonn,less

AUTHOR

R. J. Mathar, Oct 18 2009

STATUS

approved

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Last modified March 26 19:03 EDT 2019. Contains 321511 sequences. (Running on oeis4.)