

A253826


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


4



1, 18, 595, 20196, 686053, 23305590, 791703991, 26894630088, 913625718985, 31036379815386, 1054323288004123, 35815955412324780, 1216688160731038381, 41331581509442980158, 1404057083160330286975, 47696609245941786776976, 1620280657278860420130193
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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^28y^22x+8y2=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(n1)35*a(n2)+a(n3).
G.f.: x*(17*x1) / ((x1)*(x^234*x+1)).
a(n) = sqrt((2(1712*sqrt(2))^n(17+12*sqrt(2))^n)*(2(1712*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*x1)/((x1)*(x^234*x+1)) + O(x^100))


CROSSREFS

Cf. A000217, A008843, A016754, A046177.
Sequence in context: A177098 A133401 A211708 * A061079 A180822 A295369
Adjacent sequences: A253823 A253824 A253825 * A253827 A253828 A253829


KEYWORD

nonn,easy


AUTHOR

Colin Barker, Jan 16 2015


STATUS

approved



