A273365 Numbers k such that 10*k+4 is a perfect square.

0, 6, 14, 32, 48, 78, 102, 144, 176, 230, 270, 336, 384, 462, 518, 608, 672, 774, 846, 960, 1040, 1166, 1254, 1392, 1488, 1638, 1742, 1904, 2016, 2190, 2310, 2496, 2624, 2822, 2958, 3168, 3312, 3534, 3686, 3920, 4080, 4326, 4494

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 + 4*n, n>=0.

a(2n-1) = 10*n^2 - 4*n, n>=1.

G.f.: 2*x*(3*x^2+4x+3)/((1-x)^3*(1+x)^2).

From G. C. Greubel, May 21 2016: (Start)

E.g.f.: (1/2)*((5*x^2 + 11*x)*cosh(x) + (5*x^2 + 9*x + 1)*sinh(x)).

a(n) = a(n-1) + 2*a(n-2) - 2*a(n-3) - a(n-4) + a(n-5). (End)

Mathematica

LinearRecurrence[{1, 2, -2, -1, 1}, {0, 6, 14, 32, 48}, 50] (* G. C. Greubel, May 21 2016 *)
Select[Range[0, 5000], IntegerQ[Sqrt[10#+4]]&] (* Harvey P. Dale, Apr 19 2019 *)

Prog

(PARI) is(n)=issquare(10*n+4) \\ Charles R Greathouse IV, Jan 31 2017

Crossrefs

Cf. A132356, A273366, A273367, A273368.

Cf. A033583 (perfect squares ending in 0 in base 10 with final 0 removed).

Sequence in context: A134067 A350107 A024932 * A271996 A199705 A225972

Adjacent sequences: A273362 A273363 A273364 * A273366 A273367 A273368

Keyword

nonn,easy

Author

Nathan Fox, Brooke Logan, and N. J. A. Sloane, May 20 2016

Status

approved