A253826 Indices of centered octagonal numbers (A016754) which are also triangular numbers (A000217).

1, 18, 595, 20196, 686053, 23305590, 791703991, 26894630088, 913625718985, 31036379815386, 1054323288004123, 35815955412324780, 1216688160731038381, 41331581509442980158, 1404057083160330286975, 47696609245941786776976, 1620280657278860420130193

Offset

1,2

Comments

Also positive integers y in the solutions to x^2 - 8*y^2 + x + 8*y - 2 = 0, the corresponding values of x being A008843.

Also the indices of centered octagonal numbers (A016754) which are also hexagonal numbers (A000384). Also positive numbers y in the solutions to 4x^2-8y^2-2x+8y-2=0. - Colin Barker, Jan 25 2015

Links

Colin Barker, Table of n, a(n) for n = 1..654

Index entries for linear recurrences with constant coefficients, signature (35,-35,1).

Formula

a(n) = 35*a(n-1)-35*a(n-2)+a(n-3).

G.f.: x*(17*x-1) / ((x-1)*(x^2-34*x+1)).

a(n) = sqrt((-2-(17-12*sqrt(2))^n-(17+12*sqrt(2))^n)*(2-(17-12*sqrt(2))^(1+n)-(17+12*sqrt(2))^(1+n)))/(8*sqrt(2)). - Gerry Martens, Jun 04 2015

Example

18 is in the sequence because the 18th centered octagonal number is 1225, which is also the 49th triangular number.
18 is in the sequence because the 18th centered octagonal number 1225 is also the 25th hexagonal number. - Colin Barker, Jan 25 2015

Prog

(PARI) Vec(x*(17*x-1)/((x-1)*(x^2-34*x+1)) + O(x^100))

Crossrefs

Cf. A000217, A008843, A016754, A046177.

Sequence in context: A133401 A211708 A341305 * A061079 A180822 A295369

Adjacent sequences: A253823 A253824 A253825 * A253827 A253828 A253829

Keyword

nonn,easy

Author

Colin Barker, Jan 16 2015

Status

approved