

A253674


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


3



1, 10, 40, 931, 3871, 91180, 379270, 8934661, 37164541, 875505550, 3641745700, 85790609191, 356853914011, 8406604195120, 34968041827330, 823761420512521, 3426511245164281, 80720212606031890, 335763133984272160, 7909757073970612651, 32901360619213507351
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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(n1)+98*a(n2)98*a(n3)a(n4)+a(n5).
G.f.: x*(x^25*x+1)*(x^2+14*x+1) / ((x1)*(x^210*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^25*x+1)*(x^2+14*x+1)/((x1)*(x^210*x+1)*(x^2+10*x+1)) + O(x^100))


CROSSREFS

Cf. A005448, A016754, A253673, A253675.
Sequence in context: A054885 A000449 A027274 * A016082 A003355 A247201
Adjacent sequences: A253671 A253672 A253673 * A253675 A253676 A253677


KEYWORD

nonn,easy


AUTHOR

Colin Barker, Jan 08 2015


STATUS

approved



