login
A249483
Squares (A000290) which are also centered triangular numbers (A005448).
3
1, 4, 64, 361, 6241, 35344, 611524, 3463321, 59923081, 339370084, 5871850384, 33254804881, 575381414521, 3258631508224, 56381506772644, 319312633001041, 5524812282304561, 31289379402593764, 541375222159074304, 3066039868821187801, 53049246959306977201
OFFSET
1,2
COMMENTS
Apart from the first term the same as A165516. - R. J. Mathar, Jan 20 2015
FORMULA
a(n) = a(n-1)+98*a(n-2)-98*a(n-3)-a(n-4)+a(n-5).
G.f.: -x*(x^2-5*x+1)*(x^2+8*x+1) / ((x-1)*(x^2-10*x+1)*(x^2+10*x+1)).
EXAMPLE
64 is in the sequence because the 8th square is 64, which is also the 7th centered triangular number.
MATHEMATICA
CoefficientList[Series[(x^2 - 5 x + 1) (x^2 + 8 x + 1) / ((1 - x) (x^2 - 10 x + 1) (x^2 + 10 x + 1)), {x, 0, 70}], x] (* Vincenzo Librandi, Jan 20 2015 *)
PROG
(PARI) Vec(-x*(x^2-5*x+1)*(x^2+8*x+1)/((x-1)*(x^2-10*x+1)*(x^2+10*x+1)) + O(x^100))
(Magma) I:=[1, 4, 64, 361, 6241]; [n le 5 select I[n] else Self(n-1)+98*Self(n-2)-98*Self(n-3)-Self(n-4)+Self(n-5): n in [1..50]]; // Vincenzo Librandi, Jan 20 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Colin Barker, Jan 13 2015
STATUS
approved