A253674 Indices of centered octagonal numbers (A016754) which are also centered triangular numbers (A005448).

1, 10, 40, 931, 3871, 91180, 379270, 8934661, 37164541, 875505550, 3641745700, 85790609191, 356853914011, 8406604195120, 34968041827330, 823761420512521, 3426511245164281, 80720212606031890, 335763133984272160, 7909757073970612651, 32901360619213507351

Offset

1,2

Comments

Also positive integers y in the solutions to 3*x^2 - 8*y^2 - 3*x + 8*y = 0, the corresponding values of x being A253673.

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+14*x+1) / ((x-1)*(x^2-10*x+1)*(x^2+10*x+1)).

Example

10 is in the sequence because the 10th centered octagonal number is 361, which is also the 16th centered triangular number.

Mathematica

LinearRecurrence[{1, 98, -98, -1, 1}, {1, 10, 40, 931, 3871}, 30] (* Harvey P. Dale, Oct 01 2015 *)

Prog

(PARI) Vec(-x*(x^2-5*x+1)*(x^2+14*x+1)/((x-1)*(x^2-10*x+1)*(x^2+10*x+1)) + O(x^100))

Crossrefs

Cf. A005448, A016754, A253673, A253675.

Sequence in context: A054885 A000449 A027274 * A016082 A346346 A003355

Adjacent sequences: A253671 A253672 A253673 * A253675 A253676 A253677

Keyword

nonn,easy

Author

Colin Barker, Jan 08 2015

Status

approved