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

1,2

Comments

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

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).

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

Cf. A000290, A005448, A129444, A129445.

Sequence in context: A141046 A264055 A222557 * A165516 A064935 A030098

Adjacent sequences: A249480 A249481 A249482 * A249484 A249485 A249486

Keyword

nonn,easy

Author

Colin Barker, Jan 13 2015

Status

approved