

A203624


Numbers which are both decagonal and octagonal.


2



1, 54405, 2047494625, 77055412679701, 2899903398740389665, 109134964431140411989765, 4107185248501634866082443201, 154569809532975562119006255453525, 5817080207856817056285046551655533505, 218919996387913643563255879805998092490501
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OFFSET

1,2


COMMENTS

As n increases, this sequence is approximately geometric with common ratio r = lim(n>Infinity, a(n)/a(n1)) = (2+sqrt(3))^8 = 18817+10864*sqrt(3).


LINKS

Table of n, a(n) for n=1..10.
Index entries for linear recurrences with constant coefficients, signature (37635, 37635, 1).


FORMULA

G.f.: x*(1+16770*x+85*x^2) / ((1x)*(137634*x+x^2)).
a(n) = 37634*a(n1)a(n2)+16856.
a(n) = 37635*a(n1)37635*a(n2)+a(n3).
a(n) = 1/192*((13+4*sqrt(3))*(2+sqrt(3))^(8*n6)+(134*sqrt(3))*(2sqrt(3))^(8*n6)86).
a(n) = floor(1/192*(13+4*sqrt(3))*(2+sqrt(3))^(8*n6)).


EXAMPLE

The second octagonal number that is also decagonal is 54405. Hence a(2)=54405.


MATHEMATICA

LinearRecurrence[{37635, 37635, 1}, {1, 54405, 2047494625}, 10]


CROSSREFS

Cf. A203625, A203626, A001107, A000567.
Sequence in context: A202315 A270763 A251479 * A250857 A083616 A235104
Adjacent sequences: A203621 A203622 A203623 * A203625 A203626 A203627


KEYWORD

nonn,easy


AUTHOR

Ant King, Jan 05 2012


STATUS

approved



