A109020 (2*7^n - 3*3^n + 1)/6.

0, 1, 12, 101, 760, 5481, 38852, 273421, 1918320, 13441361, 94128892, 659020341, 4613496680, 32295539641, 226071966132, 1582513328861, 11077621999840, 77543440092321, 542804338926572, 3799631147326981, 26597420355811800, 186181949464251401, 1303273667170466212

Offset: 0

Author

Alex Fink and R. K. Guy, Aug 18 2005

Keywords

• nonn

Comments

Number of incongruent integer-edged Heron triangles whose circumdiameter is the product of n distinct primes of shape 4k + 1.

Links

• Index entries for linear recurrences with constant coefficients, signature (11, -31, 21).

Programs

Mathematica

Table[(2*7^n-3*3^n+1)/6,{n,0,30}] (* or *) LinearRecurrence[{11,-31,21},{0,1,12},30] (* Harvey P. Dale, Aug 10 2012 *)

Formula

a(0)=0, a(1)=1, a(2)=12, a(n)=11*a(n-1)-31*a(n-2)+21*a(n-3) -- From Harvey P. Dale, Aug 10 2012

G.f.: (-x^2-x)/(21*x^3-31*x^2+11*x-1) -- From Harvey P. Dale, Aug 10 2012