

A202565


Indices of decagonal numbers which are also pentagonal.


2



1, 56, 5451, 534106, 52336901, 5128482156, 502538914351, 49243685124206, 4825378603257801, 472837859434140256, 46333284845942487251, 4540189077042929610306, 444892196265361159322701, 43594895044928350684014356, 4271854822206713005874084151
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OFFSET

1,2


COMMENTS

As n increases, this sequence is approximately geometric with common ratio r = lim(n>oo, a(n)/a(n1)) = (sqrt(3)+sqrt(2))^4 = 49+20*sqrt(6).


LINKS



FORMULA

G.f.: x*(143*x+6*x^2) / ((1x)*(198*x+x^2)).
a(n) = 98*a(n1)a(n2)36.
a(n) = 99*a(n1)99*a(n2)+a(n3).
a(n) = 1/48*(5*sqrt(3)*((sqrt(3)+sqrt(2))^(4n3)+(sqrt(3)sqrt(2))^(4n3))+18).
a(n) = ceiling(5/48*sqrt(3)*(sqrt(3)+sqrt(2))^(4n3)).


EXAMPLE

The second decagonal number that is also pentagonal is A001107(56) = 12376. Hence a(2)=56.


MATHEMATICA

LinearRecurrence[{99, 99, 1}, {1, 56, 5451}, 15]


CROSSREFS



KEYWORD

nonn,easy


AUTHOR



STATUS

approved



