

A253470


Indices of centered triangular numbers (A005448) which are also centered pentagonal numbers (A005891).


2



1, 5, 36, 280, 2201, 17325, 136396, 1073840, 8454321, 66560725, 524031476, 4125691080, 32481497161, 255726286205, 2013328792476, 15850904053600, 124793903636321, 982500325036965, 7735208696659396, 60899169248238200, 479458145289246201, 3774765993065731405
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OFFSET

1,2


COMMENTS

Also indices of pentagonal numbers (A000326) which are also centered pentagonal numbers (A005891).
Also positive integers x in the solutions to 3*x^2  5*y^2  3*x + 5*y = 0, the corresponding values of y being A182432.


LINKS

Colin Barker, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (9,9,1).


FORMULA

a(n) = 9*a(n1)9*a(n2)+a(n3).
G.f.: x*(4*x1) / ((x1)*(x^28*x+1)).
a(n) = (6(4sqrt(15))^n*(3+sqrt(15))+(3+sqrt(15))*(4+sqrt(15))^n)/12.  Colin Barker, Mar 03 2016


EXAMPLE

5 is in the sequence because the 5th centered triangular number is 31, which is also the 4th centered pentagonal number.


PROG

(PARI) Vec(x*(4*x1)/((x1)*(x^28*x+1)) + O(x^100))


CROSSREFS

Cf. A005448, A005891, A182432, A253654.
Sequence in context: A285392 A327091 A201351 * A188899 A052203 A332624
Adjacent sequences: A253467 A253468 A253469 * A253471 A253472 A253473


KEYWORD

nonn,easy


AUTHOR

Colin Barker, Jan 01 2015


STATUS

approved



