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A225786 Numbers k such that oblong(2*k) + oblong(k) is a square, where oblong(k) = A002378(k) = k*(k+1). 2
0, 48, 15552, 5007792, 1612493568, 519217921200, 167186558132928, 53833552500881712, 17334236718725778432, 5581570389877199773488, 1797248331303739601284800, 578708381109414274413932208, 186342301468900092621684886272 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Numbers k such that k*(5*k+3) is a perfect square. Apparently a(n) = 323*a(n-1) -323*a(n-2) +a(n-3). - R. J. Mathar, May 18 2013

LINKS

Table of n, a(n) for n=1..13.

Index entries for linear recurrences with constant coefficients, signature (323,-323,1).

FORMULA

G.f.: 48*x*(1+x)/((1-x)*(1-322*x+x^2)). - Bruno Berselli, May 18 2013

a(n) = (3/20)*((2-sqrt(5))^(4n-4)+(2+sqrt(5))^(4n-4)-2). - Bruno Berselli, May 18 2013

EXAMPLE

48*49 + 96*97 = 108^2, so 48 is in the sequence.

MATHEMATICA

LinearRecurrence[{323, -323, 1}, {0, 48, 15552}, 15] (* Bruno Berselli, May 18 2013 *)

PROG

(C)

#include <stdio.h>

#include <math.h>

int main() {

  unsigned long long i, s, t;

  for (i = 0; i< (1ULL<<31); i++) {

    s = 2*i*(2*i+1) + i*(i+1);

    t = sqrt(s);

    if (s==t*t) printf("%llu, ", i);

  }

  return 0;

}

CROSSREFS

Cf. A002378.

Cf. A098301 (numbers n such that oblong(2*n) - oblong(n) is a square).

Cf. A224419 (triangular(2*n) + triangular(n) is a square).

Cf. A220186 (triangular(2*n) - triangular(n) is a square).

Cf. A225785 (oblong(2*n) + oblong(n) is an oblong number).

Sequence in context: A123478 A275570 A307618 * A275454 A202928 A265866

Adjacent sequences:  A225783 A225784 A225785 * A225787 A225788 A225789

KEYWORD

nonn,easy

AUTHOR

Alex Ratushnyak, May 16 2013

EXTENSIONS

a(6) from Ralf Stephan, May 17 2013

More terms from Bruno Berselli, May 18 2013

STATUS

approved

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Last modified August 8 16:31 EDT 2022. Contains 356016 sequences. (Running on oeis4.)