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A154147 Indices k such that 19 plus the k-th triangular number is a perfect square. 3
3, 9, 30, 60, 179, 353, 1046, 2060, 6099, 12009, 35550, 69996, 207203, 407969, 1207670, 2377820, 7038819, 13858953, 41025246, 80775900, 239112659, 470796449, 1393650710, 2744002796, 8122791603, 15993220329, 47343098910, 93215319180, 275935801859 (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: 19+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*(3 +6*x +3*x^2 -6*x^3 -4*x^4)/((1-x) * (x^2-2*x-1) * (x^2+2*x-1)).

EXAMPLE

3*(3+1)/2+19 = 5^2. 9*(9+1)/2+19 = 8^2. 30*(30+1)/2+19 = 22^2. 60*(60+1)/2+19 = 43^2.

MATHEMATICA

Join[{3, 9}, Select[Range[0, 10^5], ( Ceiling[Sqrt[#*(# + 1)/2]] )^2 - #*(# + 1)/2 == 19 &]] (* or *) LinearRecurrence[{1, 6, -6, -1, 1}, {3, 9, 30, 60, 179}, 25] (* G. C. Greubel, Sep 03 2016 *)

PROG

(PARI) {for (n=0, 10^9, if ( issquare(n*(n+1)\2 + 19), print1(n, ", ") ) ); }

CROSSREFS

Cf. A000217, A000290, A006451.

Sequence in context: A292756 A151451 A138938 * A179545 A163129 A074003

Adjacent sequences:  A154144 A154145 A154146 * A154148 A154149 A154150

KEYWORD

nonn,less

AUTHOR

R. J. Mathar, Oct 18 2009

STATUS

approved

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Last modified June 7 02:48 EDT 2020. Contains 334836 sequences. (Running on oeis4.)