Search: id:A086901
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%I A086901
%S A086901 1,1,7,31,145,673,3127,14527,67489,313537,1456615,6767071,31438129,
%T A086901 146053729,678529303,3152278399,14644701505,68035641217,316076669383,
%U A086901 1468413601183,6821884412881,31692778455073,147236767058935
%N A086901 a(1) = a(2) = 1; for n>2, a(n) = 4*a(n-1) + 3*a(n-2).
%F A086901 a(n) = [(c + 5)b^n - (b + 5)c^n]/14, where b = 2 + sqrt(7), c = 2 - sqrt(7)
%F A086901 G.f.: x(1-3x)/(1-4x-3x^2). a(n) = A015530(n) - 3*A015530(n-1) = 1 + 6*sum(k=0, 
               n, A015530(k)). - Ralf Stephan (ralf(AT)ark.in-berlin.de), Feb 01 
               2004
%F A086901 a(n+1)=Sum_{k,0<=k<=n}3^(n-k)*A122542(n,k), n>=0 . - Philippe DELEHAM 
               (kolotoko(AT)wanadoo.fr), Oct 27 2006
%F A086901 a(n) = upper left term in the 2 X 2 matrix [1,2; 3,3]^(n-1) - Gary W. 
               Adamson (qntmpkt(AT)yahoo.com), Mar 02 2008
%F A086901 a(n)=(1/14)*[2-sqrt(7)]^n*sqrt(7)-(1/14)*sqrt(7)*[2+sqrt(7)]^n+(1/2)*[2-sqrt(7)]^n+(1/
               2)*[2 +sqrt(7)]^n, with n>=0 [From Paolo P. Lava (ppl(AT)spl.at), 
               Nov 20 2008]
%e A086901 a(3) = 4(1) + 3(1) = 7; a(4) = 4(7) + 3(1) = 31.
%Y A086901 Sequence in context: A001896 A044049 A005825 this_sequence A003526 A121517 
               A057620
%Y A086901 Adjacent sequences: A086898 A086899 A086900 this_sequence A086902 A086903 
               A086904
%K A086901 easy,nonn
%O A086901 1,3
%A A086901 Rick Powers (rick.powers(AT)mnsu.edu), Sep 18 2003
%E A086901 More terms from Ray Chandler (rayjchandler(AT)sbcglobal.net), Sep 19 
               2003

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