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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.)