A273368 - OEIS

%I #17 Nov 08 2018 11:14:48

%S 0,4,16,28,52,72,108,136,184,220,280,324,396,448,532,592,688,756,864,

%T 940,1060,1144,1276,1368,1512,1612,1768,1876,2044,2160,2340,2464,2656,

%U 2788,2992,3132,3348,3496,3724,3880,4120,4284,4536

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

%H G. C. Greubel, <a href="/A273368/b273368.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1, 2, -2, -1, 1).

%F a(2n) = 10*n^2 + 6*n, n>=0.

%F a(2n-1) = 10*n^2 - 6*n, n>=1.

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

%F From _G. C. Greubel_, May 21 2016: (Start)

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

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

%F a(n) = 4*A085787(n). - _R. J. Mathar_, Jun 03 2016

%t 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 *)

%o (PARI) is(n)=issquare(10*n+9) \\ _Charles R Greathouse IV_, Jan 31 2017

%Y Cf. A132356, A273365, A273366, A273367.

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

%K nonn,easy

%O 0,2

%A _Nathan Fox_, _Brooke Logan_, and _N. J. A. Sloane_, May 20 2016