OFFSET
1,1
COMMENTS
Largest perimeter of any triangle with integer sides a<=b<=c and inradius n. Triangle has sides (n^2+2,n^4+2n^2+1,n^4+3n^2+1).
LINKS
David W. Wilson, Table of n, a(n) for n = 1..10000
Index entries for linear recurrences with constant coefficients, signature (5, -10, 10, -5, 1).
FORMULA
From Chai Wah Wu, Apr 15 2017: (Start)
a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n > 5.
G.f.: x*(-4*x^4 + 8*x^3 - 40*x^2 - 12)/(x - 1)^5. (End)
MATHEMATICA
LinearRecurrence[{5, -10, 10, -5, 1}, {12, 60, 220, 612, 1404}, 40] (* Harvey P. Dale, Dec 28 2018 *)
PROG
(PARI) a(n)=2*(n^2+1)*(n^2+2) \\ Charles R Greathouse IV, Oct 21 2022
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
David W. Wilson, Jun 17 2006
STATUS
approved