|
%I #27 Oct 25 2023 07:39:01
%S 1,12,109,888,6841,51012,372709,2687088,19200241,136354812,964249309,
%T 6798573288,47834153641,336059778612,2358521965909,16540171339488,
%U 115933787267041,812299450322412,5689910849522509
%N Expansion of g.f. 1/((1-5*x)*(1-7*x)).
%C Also, this is the number of incongruent integer-edged Heron triangles whose circumdiameter is the product of n distinct primes each of shape 4k + 1. Cf. A003462, A109021. - _R. K. Guy_, Jan 31 2007
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (12,-35).
%F From _R. J. Mathar_, Sep 18 2008: (Start)
%F a(n) = (7^(n+1)-5^(n+1))/2 = A081200(n+1).
%F Binomial transform of A080962. (End)
%F a(n) = 7*a(n-1) + 5^n. - _Vincenzo Librandi_, Feb 09 2011
%F E.g.f.: exp(5*x)*(7*exp(2*x) - 5)/2. - _Stefano Spezia_, Oct 25 2023
%t CoefficientList[Series[1/((1-5x)(1-7x)),{x,0,30}],x] (* or *) LinearRecurrence[ {12,-35},{1,12},30] (* _Harvey P. Dale_, Nov 16 2021 *)
%o (PARI) Vec(1/((1-5*x)*(1-7*x))+O(x^99)) \\ _Charles R Greathouse IV_, Sep 24 2012
%Y Cf. A003462, A080962, A081200, A109021.
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_
|
