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

%I

%S 0,1,12,101,760,5481,38852,273421,1918320,13441361,94128892,659020341,

%T 4613496680,32295539641,226071966132,1582513328861,11077621999840,

%U 77543440092321,542804338926572,3799631147326981,26597420355811800,186181949464251401,1303273667170466212

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

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

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (11, -31, 21).

%F 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

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

%t 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 *)

%K nonn

%O 0,3

%A _Alex Fink_ and _R. K. Guy_, Aug 18 2005

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Last modified September 22 15:04 EDT 2021. Contains 347607 sequences. (Running on oeis4.)