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 1/81*(216401+68432*sqrt(10)) and 1/81*(15761+4984*sqrt(10)) respectively.
LINKS
Index entries for linear recurrences with constant coefficients, signature (1,2079362,-2079362,-1,1).
FORMULA
G.f.: x(1+539*x+807548*x^2+10633*x^3+27*x^4) / ((1-x)*(1-1442*x+x^2)*(1+1442*x+x^2)).
a(n) = 2079362*a(n-2)-a(n-4)+818748.
a(n) = a(n-1)+2079362*a(n-2)-2079362*a(n-3)-a(n-4)+a(n-5).
a(n) = 1/320*((11-2*sqrt(10)*(-1)^n)*(1+sqrt(10))* (3+sqrt(10))^(4*n-3)+(11+2*sqrt(10)*(-1)^n)*(1-sqrt(10))*(3-sqrt(10))^(4*n-3)-126).
a(n) = floor(1/320*(11-2*sqrt(10)*(-1)^n)*(1+sqrt(10))* (3+sqrt(10))^(4*n-3)).
EXAMPLE
The second number that is both heptagonal and decagonal is 540. Hence a(2)=540.
MATHEMATICA
LinearRecurrence[{1, 2079362, -2079362, -1, 1}, {1, 540, 2887450, 1123674201, 6004054625647}, 15]
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Ant King, Jan 02 2012
STATUS
approved