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 A273368 Numbers k such that 10*k+9 is a perfect square. 5
 0, 4, 16, 28, 52, 72, 108, 136, 184, 220, 280, 324, 396, 448, 532, 592, 688, 756, 864, 940, 1060, 1144, 1276, 1368, 1512, 1612, 1768, 1876, 2044, 2160, 2340, 2464, 2656, 2788, 2992, 3132, 3348, 3496, 3724, 3880, 4120, 4284, 4536 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS G. C. Greubel, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (1, 2, -2, -1, 1). FORMULA a(2n) = 10*n^2 + 6*n, n>=0. a(2n-1) = 10*n^2 - 6*n, n>=1. G.f.: 4*x*(x^2+3x+1)/((1-x)^3*(1+x)^2). From G. C. Greubel, May 21 2016: (Start) E.g.f.: (1/2)*((5*x^2 + 9*x)*cosh(x) + (5*x^2 + 11*x -1)*sinh(x)). a(n) = a(n-1) + 2*a(n-2) - 2*a(n-3) - a(n-4) + a(n-5). (End) a(n) = 4*A085787(n). - R. J. Mathar, Jun 03 2016 MATHEMATICA CoefficientList[Series[4*x*(x^2+3x+1)/((1-x)^3*(1+x)^2), {x, 0, 50}], x] (* or *) LinearRecurrence[{1, 2, -2, -1, 1}, {0, 4, 16, 28, 52}, 50] (* G. C. Greubel, May 20 2016 *) PROG (PARI) is(n)=issquare(10*n+9) \\ Charles R Greathouse IV, Jan 31 2017 CROSSREFS Cf. A132356, A273365, A273366, A273367. Cf. A033583 (perfect squares ending in 0 in base 10 with final 0 removed). Sequence in context: A161335 A121054 A332044 * A209979 A294629 A160410 Adjacent sequences:  A273365 A273366 A273367 * A273369 A273370 A273371 KEYWORD nonn,easy AUTHOR Nathan Fox, Brooke Logan, and N. J. A. Sloane, May 20 2016 STATUS approved

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Last modified March 29 15:16 EDT 2020. Contains 333107 sequences. (Running on oeis4.)