OFFSET
1,2
COMMENTS
As n increases, this sequence is approximately geometric with common ratio (1+sqrt(2))^4=17+12*sqrt(2).
LINKS
Index entries for linear recurrences with constant coefficients, signature (35, -35, 1).
FORMULA
G.f.: x(1-7*x-2*x^2) / ((1-x)*(1-34*x+x^2))
a(n) = 35*a(n-1)-35*a(n-2)+a(n-3)
a(n) = 34*a(n-1)-a(n-2)-8
a(n) = 1/16 *((3*sqrt(2)-2)*(1+sqrt(2))^(4*n-2)- (3*sqrt(2)+2)*(1-sqrt(2))^(4*n-2)+4)
a(n) = ceiling(1/16 *(3*sqrt(2)-2)*(1+sqrt(2))^(4*n-2))
EXAMPLE
The second hexagonal number which is also decagonal is A000384(28)=1540. Hence a(2) = 28.
MATHEMATICA
LinearRecurrence[{35, -35, 1}, {1, 28, 943}, 17]
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Ant King, Dec 30 2011
STATUS
approved