

A203136


Indices of decagonal numbers that are also hexagonal.


2



1, 20, 667, 22646, 769285, 26133032, 887753791, 30157495850, 1024467105097, 34801724077436, 1182234151527715, 40161159427864862, 1364297186395877581, 46345943178031972880, 1574397770866691200327, 53483178266289468838226, 1816853663282975249299345
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OFFSET

1,2


COMMENTS

As n increases, this sequence is approximately geometric with common ratio (1+sqrt(2))^4=17+12*sqrt(2).


LINKS



FORMULA

G.f.: x(115*x+2*x^2) / ((1x)*(134*x+x^2))
a(n) = 35*a(n1)35*a(n2)+a(n3)
a(n) = 34*a(n1)a(n2)12
a(n) = 1/16 *((3sqrt(2))*(1+sqrt(2))^(4*n2)+(3+sqrt(2))*(1sqrt(2))^(4*n2)+6)
a(n) = ceiling(1/16*(3sqrt(2))*(1+sqrt(2))^(4*n2))


EXAMPLE

The second decagonal number which is also hexagonal is A001107(20) = 1540. Hence a(2) = 20.


MATHEMATICA

LinearRecurrence[{35, 35, 1}, {1, 20, 667}, 17]


CROSSREFS



KEYWORD

nonn,easy


AUTHOR



STATUS

approved



