A120573 a(n) = n^5 + 3n^3 + 2n = n(n^2+1)(n^2+2).

6, 60, 330, 1224, 3510, 8436, 17850, 34320, 61254, 103020, 165066, 254040, 377910, 546084, 769530, 1060896, 1434630, 1907100, 2496714, 3224040, 4111926, 5185620, 6472890, 8004144, 9812550, 11934156, 14408010, 17276280, 20584374, 24381060

Offset: 1

Author

David W. Wilson, Jun 17 2006

Keywords

• nonn
• easy

Comments

Largest area 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).

a(n) = A002522(n)*A054602(n). - Zerinvary Lajos, Apr 20 2008

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).

Crossrefs

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

Cf. A002522, A054602.

Programs

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 *)