OFFSET
1,2
COMMENTS
As n increases, the ratios of consecutive terms settle into an approximate 2-cycle with a(n)/a(n-1) bounded above and below by 1/9*(329+104*sqrt(10)) and 1/9*(89+28*sqrt(10)) respectively.
LINKS
Index entries for linear recurrences with constant coefficients, signature (1,1442,-1442,-1,1).
FORMULA
G.f.: x*(1+14*x-382*x^2-62*x^3-3*x^4) / ((1-x)*(1-38*x+x^2)*(1+38*x+x^2)).
a(n) = 1442*a(n-2)-a(n-4)-432.
a(n) = a(n-1)+1442*a(n-2)-1442*a(n-3)-a(n-4)+a(n-5).
a(n) = 1/40*(((-1)^n-sqrt(10))*(2-sqrt(10))*(3+sqrt(10))^(2*n-1)+((-1)^n+sqrt(10))*(2+sqrt(10))*(3-sqrt(10))^(2*n-1)+12).
a(n) = ceiling(1/40*((-1)^n-sqrt(10))*(2-sqrt(10))*(3+sqrt(10))^(2*n-1)).
EXAMPLE
The second heptagonal number that is also decagonal is A000566(15)=540. Hence a(2)=15.
MATHEMATICA
LinearRecurrence[{1, 1442, -1442, -1, 1}, {1, 15, 1075, 21201, 1549717}, 17]
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Ant King, Jan 02 2012
STATUS
approved