OFFSET
1,2
COMMENTS
Also, numbers of the form 25m^2+12*m, where m = 0,-1,1,-2,2,-3,3,... - Bruno Berselli, Apr 07 2013
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (1,2,-2,-1,1).
FORMULA
G.f.: x^2*(13+24*x+13*x^2)/((1+x)^2*(1-x)^3).
a(n) = (50*n*(n-1)+(2*n-1)*(-1)^n+1)/8.
a(n) = a(n-1)+2*a(n-2)-2*a(n-3)-a(n-4)+a(n-5).
Sum_{n>=2} 1/a(n) = 25/144 - tan(Pi/50)*Pi/12. - Amiram Eldar, Feb 16 2023
MATHEMATICA
Select[Range[0, 10000], IntegerQ[Sqrt[25 # + 36]]&] (* or *) CoefficientList[Series[x (13 + 24 x + 13 x^2)/((1+x)^2(1-x)^3), {x, 0, 40}], x]
PROG
(Magma) [n: n in [0..15000] | IsSquare(25*n+36)]; /* or */ I:=[0, 13, 37, 76, 124]; [n le 5 select I[n] else Self(n-1)+2*Self(n-2)-2*Self(n-3)-Self(n-4)+Self(n-5): n in [1..50]];
(Magma) [0] cat [25*m^2+12*m where m is n*t: t in [-1, 1], n in [1..20]]; // Bruno Berselli, Apr 07 2013
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Apr 07 2013
STATUS
approved