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%I #17 Jan 27 2020 01:36:08
%S 1,6,73,882,10657,128766,1555849,18798954,227143297,2744518518,
%T 33161365513,400680904674,4841332221601,58496667563886,
%U 706801342988233,8540112783422682,103188154744060417,1246797969712147686
%N a(n) = 12*a(n-1) + a(n-2), a(0)=1, a(1)=6.
%C The family of recurrences a(n) = 2*k*a(n-1) + a(n-2), a(0)=1, a(1)=k has solution a(n) = ((k+sqrt(k^2+1))^n + (k-sqrt(k^2+1))^n)/2; a(n) = Sum_{j=0..floor(n/2)} C(n,2k)*(k^2+1)^jk^(n-2j); a(n) = T(n,ki)*(-i)^n; e.g.f. exp(kx)*cosh(sqrt(k^2+1)*x).
%H Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>
%H <a href="/index/Ch#Cheby">Index entries for sequences related to Chebyshev polynomials.</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (12,1).
%F E.g.f.: exp(6x)*cosh(sqrt(37)x);
%F a(n) = ((6+sqrt(37))^n + (6-sqrt(37))^n)/2;
%F a(n) = Sum_{k=0..floor(n/2)} C(n, 2k)*37^k*6^(n-2k).
%F a(n) = T(n, 6i)*(-i)^n with T(n, x) Chebyshev's polynomials of the first kind (see A053120) and i^2 = -1.
%F G.f.: (1-6x)/(1-12*x-x^2). - _Philippe Deléham_, Nov 21 2008
%Y Cf. A088320, A088317, A005667, A001077.
%K easy,nonn
%O 0,2
%A _Paul Barry_, Nov 15 2003
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