OFFSET
1,2
COMMENTS
As n increases, this sequence is approximately geometric with common ratio (1+sqrt(2))^8 = 577+408*sqrt(2).
LINKS
Index entries for linear recurrences with constant coefficients, signature (1155, -1155, 1).
FORMULA
G.f.: x*(1+385*x+10*x^2) / ((1-x)*(1-1154*x+x^2)).
a(n) = 1155*a(n-1)-1155*a(n-2)+a(n-3).
a(n) = 1154*a(n-1)-a(n-2)+396.
a(n) = (1/64)*((5*sqrt(2)-1)*(sqrt(2)+1)^(8*n-5)+ (5*sqrt(2)+1)*(sqrt(2)-1)^(8*n-5)-22).
a(n) = floor(1/64 *(5*sqrt(2)-1)*(sqrt(2)+1)^(8*n-5)).
EXAMPLE
The second number which is both hexagonal and decagonal is 1540. Hence a(2) = 1540.
MATHEMATICA
LinearRecurrence[{1155, -1155, 1}, {1, 1540, 1777555}, 12]
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Ant King, Dec 30 2011
STATUS
approved