A253673 Indices of centered triangular numbers (A005448) that are also centered octagonal numbers (A016754).

1, 16, 65, 1520, 6321, 148896, 619345, 14590240, 60689441, 1429694576, 5946945825, 140095478160, 582740001361, 13727927165056, 57102573187505, 1345196766697280, 5595469432374081, 131815555209168336, 548298901799472385, 12916579213731799600

Offset

1,2

Comments

Also positive integers x in the solutions to 3*x^2 - 8*y^2 - 3*x + 8*y = 0, the corresponding values of y being A253674.

Also indices of centered square numbers (A001844) that are also octagonal numbers (A000567). - Colin Barker, Feb 10 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*(3*x-1)*(5*x^2+18*x+1) / ((x-1)*(x^2-10*x+1)*(x^2+10*x+1)).

Example

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

Mathematica

LinearRecurrence[{1, 98, -98, -1, 1}, {1, 16, 65, 1520, 6321}, 20] (* Harvey P. Dale, Aug 07 2023 *)

Prog

(PARI) Vec(x*(3*x-1)*(5*x^2+18*x+1)/((x-1)*(x^2-10*x+1)*(x^2+10*x+1)) + O(x^100))

Crossrefs

Cf. A005448, A016754, A253674, A253675.

Cf. A000567, A001844, A254895, A254896.

Sequence in context: A034720 A232050 A119285 * A041494 A057689 A045024

Adjacent sequences: A253670 A253671 A253672 * A253674 A253675 A253676

Keyword

nonn,easy

Author

Colin Barker, Jan 08 2015

Status

approved