A120571 2n^4+6n^2+4 = 2(n^2+1)(n^2+2).

12, 60, 220, 612, 1404, 2812, 5100, 8580, 13612, 20604, 30012, 42340, 58140, 78012, 102604, 132612, 168780, 211900, 262812, 322404, 391612, 471420, 562860, 667012, 785004, 918012, 1067260, 1234020, 1419612, 1625404, 1852812, 2103300, 2378380

Offset: 1

Author

David W. Wilson, Jun 17 2006

Keywords

• nonn
• easy

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).

Crossrefs

See A120062 for sequences related to integer-sided triangles with integer inradius n.

Programs

Mathematica

LinearRecurrence[{5,-10,10,-5,1},{12,60,220,612,1404},40] (* Harvey P. Dale, Dec 28 2018 *)

PARI

a(n)=2*(n^2+1)*(n^2+2) \\ Charles R Greathouse IV, Oct 21 2022

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)