OFFSET
1,1
LINKS
Ray Chandler, Table of n, a(n) for n = 1..5000 (first 100 terms from Zhining Yang)
Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).
FORMULA
From Colin Barker, Jun 28 2017: (Start)
G.f.: 12*x*(5 + 72*x + 166*x^2 + 72*x^3 + 5*x^4) / (1 - x)^6.
a(n) = 4*n*(2*n^2 + 1)*(4*n^2 + 1).
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)
a(n) = A120573(2n). - Ray Chandler, Jul 27 2017
EXAMPLE
For n = 4, a(4) = 34320 means for the largest triangles (a,b,c) = (66,4225,4289), the area is 34320 which is 4 times the perimeter 8580.
MATHEMATICA
Table[4 n (2 n^2 + 1) (4 n^2 + 1), {n, 27}] (* or *) LinearRecurrence[{6, -15, 20, -15, 6, -1}, {60, 1224, 8436, 34320, 103020, 254040}, 27] (* or *) Rest@ CoefficientList[Series[12 x (5 + 72 x + 166 x^2 + 72 x^3 + 5 x^4)/(1 - x)^6, {x, 0, 27}], x] (* Michael De Vlieger, Jul 03 2017 *)
PROG
(PARI) Vec(12*x*(5 + 72*x + 166*x^2 + 72*x^3 + 5*x^4) / (1 - x)^6 + O(x^30)) \\ Colin Barker, Jun 28 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Zhining Yang, Jun 26 2017
STATUS
approved