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A135360 a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) for n > 4, with first terms 1, 2, 4, 7.

%I A135360 #18 Oct 12 2016 02:49:11
%S A135360 1,2,4,7,12,22,44,92,192,392,784,1552,3072,6112,12224,24512,49152,
%T A135360 98432,196864,393472,786432,1572352,3144704,6290432,12582912,25167872,
%U A135360 50335744,100667392,201326592,402644992,805289984,1610596352,3221225472,6442483712,12884967424
%N A135360 a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) for n > 4, with first terms 1, 2, 4, 7.
%C A135360 Sequence identical to its fourth differences.
%C A135360 Without a(3)=7, sequence A000079 would have been obtained. - _Michel Marcus_, May 06 2015
%H A135360 G. C. Greubel, <a href="/A135360/b135360.txt">Table of n, a(n) for n = 0..1000</a>
%H A135360 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4).
%F A135360 a(n) = 2^n + A000749(n). - _Michel Marcus_, May 06 2015
%F A135360 G.f.: (1 - x)*(1 - x + x^2)/((1 - 2*x)*(1 - 2*x + 2*x^2)). [_Bruno Berselli_, May 06 2015]
%t A135360 Join[{1}, LinearRecurrence[{4, -6, 4}, {2, 4, 7}, 25]] (* _G. C. Greubel_, Oct 11 2016 *)
%o A135360 (PARI) lista(nn) = {v = vector(nn); v[1] = 1; v[2] = 2; v[3] = 4; v[4] = 7; for (k=5, nn, v[k] = 4*v[k-1]-6*v[k-2]+4*v[k-3];); v;} \\ _Michel Marcus_, May 06 2015
%Y A135360 Cf. A000079 (2^n), A000749.
%K A135360 nonn,easy
%O A135360 0,2
%A A135360 _Paul Curtz_, Dec 08 2007
%E A135360 More terms from _Michel Marcus_, May 06 2015