A109021 (2*7^n - 6*3^n + 4)/6.

0, 0, 8, 88, 720, 5360, 38488, 272328, 1915040, 13431520, 94099368, 658931768, 4613230960, 32294742480, 226069574648, 1582506154408, 11077600476480, 77543375522240, 542804145216328, 3799630566196248, 26597418612419600, 186181944234074800, 1303273651479936408

Offset

0,3

Comments

Number of incongruent integer-edged Heron triangles whose circumdiameter is the product of n distinct primes of shape 4k + 1 and which are not right-angled.

Links

Table of n, a(n) for n=0..22.

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

Formula

a(n) = 8*A016212(n-2).

(0)=0, a(1)=0, a(2)=8, a(n)=11*a(n-1)-31*a(n-2)+21*a(n-3). - Harvey P. Dale, Jan 30 2013

G.f.: -8*x^2 / ( (x-1)*(3*x-1)*(7*x-1) ). - R. J. Mathar, Feb 10 2016

Mathematica

Table[(2*7^n-6*3^n+4)/6, {n, 0, 30}] (* or *) LinearRecurrence[{11, -31, 21}, {0, 0, 8}, 30] (* Harvey P. Dale, Jan 30 2013 *)

Crossrefs

Cf. A016212, A109020, A003462.

Sequence in context: A300263 A367278 A030984 * A271939 A043043 A003492

Adjacent sequences: A109018 A109019 A109020 * A109022 A109023 A109024

Keyword

nonn,easy

Author

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

Status

approved