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%I #21 Sep 30 2023 14:03:00
%S 1,3,15,87,519,3111,18663,111975,671847,4031079,24186471,145118823,
%T 870712935,5224277607,31345665639,188073993831,1128443962983,
%U 6770663777895,40623982667367,243743896004199,1462463376025191,8774780256151143,52648681536906855,315892089221441127
%N a(n) = 7*a(n-1) - 6*a(n-2), n>1; a(0)=1, a(1)=3.
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (7,-6).
%F G.f.: (1-4*x)/(1 - 7*x + 6*x^2).
%F a(n) = Sum_{k=0..n} A147703(n,k)*2^(n-k).
%F a(n) = (1/5)*(3 + 2*6^n), with n>=0. - _Paolo P. Lava_, Dec 12 2008
%F E.g.f.: exp(x)*(3 + 2*exp(5*x))/5. - _Stefano Spezia_, Sep 30 2023
%t Table[MatrixPower[{{3,2},{3,4}},n][[1]][[1]],{n,0,44}] (* _Vladimir Joseph Stephan Orlovsky_, Feb 20 2010 *)
%t LinearRecurrence[{7,-6},{1,3},30] (* _Harvey P. Dale_, Jul 27 2021 *)
%Y Cf. A147703.
%K nonn,easy
%O 0,2
%A _Philippe Deléham_, Dec 09 2008
%E a(21)-a(23) from _Stefano Spezia_, Sep 30 2023