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%I #16 Jun 11 2023 10:55:33
%S 1,7,35,155,651,2667,10795,43435,174251,698027,2794155,11180715,
%T 44731051,178940587,715795115,2863245995,11453115051,45812722347,
%U 183251413675,733006703275,2932028910251,11728119835307,46912487729835
%N a(n) = 6*a(n-1) - 8*a(n-2) + 1 for n > 1; a(0) = 1, a(1) = 7.
%C a(n) = A006095(n+2).
%C Second binomial transform of A168642.
%C Essentially partial sums of A006516.
%H Vincenzo Librandi, <a href="/A171477/b171477.txt">Table of n, a(n) for n = 0..500</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (7, -14, 8).
%F a(n) = (8*4^n-6*2^n+1)/3.
%F G.f.: 1/((1-x)*(1-2*x)*(1-4*x)).
%F a(n) = A139250(2^(n+1) - 1). - _Omar E. Pol_, Dec 20 2012
%o (PARI) {m=23; v=concat([1, 7], vector(m-2)); for(n=3, m, v[n]=6*v[n-1]-8*v[n-2]+1); v}
%o (Magma) [(8*4^n-6*2^n+1)/3: n in [0..30]]; // _Vincenzo Librandi_, Jul 18 2011
%Y Cf. A006095 (Gaussian binomial coefficient [n, 2] for q=2), A168642 ((8*2^n+(-1)^n)/3, a(0)=1), A006516 (2^(n-1)*(2^n-1)), A171472, A171473.
%K nonn,easy
%O 0,2
%A _Klaus Brockhaus_, Dec 09 2009
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