OFFSET
1,1
COMMENTS
Largest area of any triangle with integer sides a <= b <= c and inradius n. Triangle has sides (n^2+2, n^4+2*n^2+1, n^4+3*n^2+1).
LINKS
David W. Wilson, Table of n, a(n) for n = 1..10000
Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).
FORMULA
From Elmo R. Oliveira, Sep 08 2025: (Start)
G.f.: 6*x*(1 + 4*x + 10*x^2 + 4*x^3 + x^4)/(x-1)^6.
E.g.f.: x*(6 + 24*x + 28*x^2 + 10*x^3 + x^4)*exp(x).
a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n > 6. (End)
MAPLE
with(combinat):seq(lcm(fibonacci(4, n), fibonacci(3, n)), n=1..30); # Zerinvary Lajos, Apr 20 2008
MATHEMATICA
LinearRecurrence[{6, -15, 20, -15, 6, -1}, {6, 60, 330, 1224, 3510, 8436}, 30] (* Harvey P. Dale, Aug 14 2023 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
David W. Wilson, Jun 17 2006
STATUS
approved