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%I #15 May 30 2023 12:57:55
%S 0,0,8,88,720,5360,38488,272328,1915040,13431520,94099368,658931768,
%T 4613230960,32294742480,226069574648,1582506154408,11077600476480,
%U 77543375522240,542804145216328,3799630566196248,26597418612419600,186181944234074800,1303273651479936408
%N (2*7^n - 6*3^n + 4)/6.
%C 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.
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (11, -31, 21).
%F a(n) = 8*A016212(n-2).
%F (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
%F G.f.: -8*x^2 / ( (x-1)*(3*x-1)*(7*x-1) ). - _R. J. Mathar_, Feb 10 2016
%t 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 *)
%Y Cf. A016212, A109020, A003462.
%K nonn,easy
%O 0,3
%A _Alex Fink_ and _R. K. Guy_, Aug 18 2005