

A253878


Indices of triangular numbers (A000217) which are also centered heptagonal numbers (A069099).


3



1, 22, 358, 5713, 91057, 1451206, 23128246, 368600737, 5874483553, 93623136118, 1492095694342, 23779907973361, 378986431879441, 6040003002097702, 96261061601683798, 1534136982624843073, 24449930660395805377, 389664753583708042966, 6210186126678932882086
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OFFSET

1,2


COMMENTS

Also positive integers x in the solutions to x^2  7*y^2 + x + 7*y  2 = 0, the corresponding values of y being A253879.


LINKS

Colin Barker, Table of n, a(n) for n = 1..832
Index entries for linear recurrences with constant coefficients, signature (17,17,1).


FORMULA

a(n) = 17*a(n1)17*a(n2)+a(n3).
G.f.: x*(x^2+5*x+1) / ((x1)*(x^216*x+1)).
a(n) = (2+(83*sqrt(7))^n*(3+sqrt(7))(3+sqrt(7))*(8+3*sqrt(7))^n)/4.  Colin Barker, Mar 04 2016


EXAMPLE

22 is in the sequence because the 22nd triangular number is 253, which is also the 9th centered heptagonal number.


PROG

(PARI) Vec(x*(x^2+5*x+1)/((x1)*(x^216*x+1)) + O(x^100))


CROSSREFS

Cf. A000217, A069099, A253879, A253880.
Sequence in context: A016263 A001718 A199671 * A081127 A016196 A238318
Adjacent sequences: A253875 A253876 A253877 * A253879 A253880 A253881


KEYWORD

nonn,easy


AUTHOR

Colin Barker, Jan 17 2015


STATUS

approved



