

A254709


Indices of pentagonal numbers (A000326) which are also centered square numbers (A001844).


3



1, 2, 10, 25, 137, 346, 1906, 4817, 26545, 67090, 369722, 934441, 5149561, 13015082, 71724130, 181276705, 998988257, 2524858786, 13914111466, 35166746297, 193798572265, 489809589370, 2699265900242, 6822167504881, 37595924031121, 95020535478962
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OFFSET

1,2


COMMENTS

Also positive integers x in the solutions to 3*x^2  4*y^2  x + 4*y  2 = 0, the corresponding values of y being A254710.


LINKS



FORMULA

a(n) = a(n1)+14*a(n2)14*a(n3)a(n4)+a(n5).
G.f.: x*(x^4+x^36*x^2+x+1) / ((x1)*(x^24*x+1)*(x^2+4*x+1)).


EXAMPLE

10 is in the sequence because the 10th pentagonal number is 145, which is also the 9th centered square number.


MATHEMATICA

LinearRecurrence[{1, 14, 14, 1, 1}, {1, 2, 10, 25, 137}, 30] (* Harvey P. Dale, Aug 08 2017 *)


PROG

(PARI) Vec(x*(x^4+x^36*x^2+x+1)/((x1)*(x^24*x+1)*(x^2+4*x+1)) + O(x^100))


CROSSREFS



KEYWORD

nonn,easy


AUTHOR



STATUS

approved



