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%I #20 Sep 08 2022 08:45:13
%S 1,3,8,21,54,137,344,857,2122,5229,12836,31413,76686,186833,454448,
%T 1103921,2678674,6494037,15732284,38089677,92173782,222961529,
%U 539145416,1303349513,3150038746,7611815613,18390447188,44426264421,107310084894
%N a(n) = Pell(n+2) - 2^n.
%C Binomial transform of A052955.
%C The sequence b(n) = 2*a(n), n >= -1, is an elephant sequence, see A175654. For the corner squares 24 A[5] vectors, with decimal values between 23 and 464, lead to the b(n) sequence. For the central square these vectors lead to the companion sequence A175658. - _Johannes W. Meijer_, Aug 15 2010
%H Vincenzo Librandi, <a href="/A094723/b094723.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (4,-3,-2).
%F G.f.: (1 - x - x^2)/((1-2*x)*(1 - 2*x - x^2)).
%F a(n) = ((1+sqrt(2))^n*(3*sqrt(2)/4+1) - (3*sqrt(2)/4-1)*(1-sqrt(2))^n) - 2^n.
%F a(n) = 4*a(n-1) - 3*a(n-2) - 2*a(n-3). - _Vincenzo Librandi_, Jun 24 2012
%t LinearRecurrence[{4,-3, -2},{1,3,8},40] (* _Vincenzo Librandi_, Jun 24 2012 *)
%o (Magma) I:=[1, 3, 8]; [n le 3 select I[n] else 4*Self(n-1)-3*Self(n-2)-2*Self(n-3): n in [1..30]]; // _Vincenzo Librandi_, Jun 24 2012
%Y Cf. A000129.
%K easy,nonn
%O 0,2
%A _Paul Barry_, May 23 2004
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