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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 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 #include 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.)