OFFSET
1,2
COMMENTS
As n increases, this sequence is approximately geometric with common ratio r = lim(n->Infinity, a(n)/a(n-1)) = (2+sqrt(3))^4 = 97+56*sqrt(3).
LINKS
Index entries for linear recurrences with constant coefficients, signature (195, -195, 1).
FORMULA
G.f.: x*(1-78*x+5*x^2) / ((1-x)*(1-194*x+x^2)).
a(n) = 194*a(n-1)-a(n-2)-72.
a(n) = 195*a(n-1)-195*a(n-2)+a(n-3).
a(n) = 1/48*((sqrt(3)+6)*(2+sqrt(3))^(4*n-3)-(sqrt(3)-6)*(2-sqrt(3))^(4*n-3)+18).
a(n) = ceiling(1/48*(sqrt(3)+6)*(2+sqrt(3))^(4*n-3)).
EXAMPLE
The second decagonal number that is also octagonal is A001107(117) = 54405. Hence a(2) = 117.
MATHEMATICA
LinearRecurrence[{195, -195, 1}, {1, 117, 22625}, 14]
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Ant King, Jan 05 2012
STATUS
approved