A273368 Numbers k such that 10*k+9 is a perfect square.

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

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