

A253475


Indices of centered square numbers (A001844) which are also centered hexagonal numbers (A003215).


3



1, 6, 55, 540, 5341, 52866, 523315, 5180280, 51279481, 507614526, 5024865775, 49741043220, 492385566421, 4874114620986, 48248760643435, 477613491813360, 4727886157490161, 46801248083088246, 463284594673392295, 4586044698650834700, 45397162391834954701
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OFFSET

1,2


COMMENTS

Also positive integers x in the solutions to 4*x^2  6*y^2  4*x + 6*y = 0, the corresponding values of y being A054318.
Also indices of centered hexagonal numbers (A003215) which are also hexagonal numbers (A000384).
Also indices of terms in sequence A193218 which are the square root of a sum of 5th powers (A000539).  Daniel Poveda Parrilla, Jun 10 2017


LINKS

Colin Barker, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (11,11,1).


FORMULA

a(n) = 11*a(n1)11*a(n2)+a(n3).
G.f.: x*(5*x1) / ((x1)*(x^210*x+1)).
a(n) = sqrt((2(52*sqrt(6))^n(5+2*sqrt(6))^n)*(2(52*sqrt(6))^(1+n)(5+2*sqrt(6))^(1+n)))/(4*sqrt(2)).  Gerry Martens, Jun 04 2015


EXAMPLE

6 is in the sequence because the 6th centered square number is 61, which is also the 5th centered hexagonal number.


PROG

(PARI) Vec(x*(5*x1)/((x1)*(x^210*x+1)) + O(x^100))


CROSSREFS

Cf. A000384, A000539, A001844, A003215, A054318, A193218, A253175.
Sequence in context: A295548 A198855 A318592 * A215853 A110431 A121661
Adjacent sequences: A253472 A253473 A253474 * A253476 A253477 A253478


KEYWORD

nonn,easy


AUTHOR

Colin Barker, Jan 02 2015


STATUS

approved



