A249483 Squares (A000290) which are also centered triangular numbers (A005448).

1, 4, 64, 361, 6241, 35344, 611524, 3463321, 59923081, 339370084, 5871850384, 33254804881, 575381414521, 3258631508224, 56381506772644, 319312633001041, 5524812282304561, 31289379402593764, 541375222159074304, 3066039868821187801, 53049246959306977201

Offset: 1

Author

Colin Barker, Jan 13 2015

Keywords

• nonn
• easy

Comments

Apart from the first term the same as A165516. - R. J. Mathar, Jan 20 2015

Examples

			64 is in the sequence because the 8th square is 64, which is also the 7th centered triangular number.
		

Links

• Colin Barker, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (1,98,-98,-1,1).

Crossrefs

Cf. A000290, A005448, A129444, A129445.

Programs

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

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 *)

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))

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)).