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
KEYWORD
nonn,easy
AUTHOR
STATUS
approved