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A181407 a(n) = (n-4)*(n-3)*2^(n-2).

%I A181407 #41 Nov 11 2024 22:28:51
%S A181407 3,3,2,0,0,16,96,384,1280,3840,10752,28672,73728,184320,450560,
%T A181407 1081344,2555904,5963776,13762560,31457280,71303168,160432128,
%U A181407 358612992,796917760,1761607680,3875536896,8489271296,18522046464,40265318400,87241523200,188441690112
%N A181407 a(n) = (n-4)*(n-3)*2^(n-2).
%C A181407 Binomial transform of (3, 0, -1, followed by A005563).
%C A181407 The sequence and its successive differences are:
%C A181407    3,  3,  2,   0,   0,   16,   96,  384,      a(n),
%C A181407    0, -1, -2,   0,  16,   80,  288,  896,      A178987,
%C A181407   -1, -1,  2,  16,  64,  208,  608, 2688,     -A127276,
%C A181407    0,  3, 14,  48, 144,  400, 1056, 2688,      A176027,
%C A181407    3, 11, 34,  96, 256,  656, 1632, 3968,      A084266(n+1)
%C A181407    8, 23, 62, 160, 400,  976, 2336, 5504,
%C A181407   15, 39, 98, 240, 576, 1360, 3168, 7296.
%C A181407 Division of the k-th column by abs(A174882(k)) gives
%C A181407    3,  3,  1,  0,  0,  1,  3,  3,  5,  15,  21, 14,   A064038(n-3),
%C A181407    0, -1, -1,  0,  1,  5,  9,  7, 10,  27,  35, 22,   A160050(n-3),
%C A181407   -1, -1,  1,  2,  4, 13, 19, 13, 17,  43,  53, 32,   A176126,
%C A181407    0,  3,  7,  6,  9, 25, 33, 21, 26,  63,  75, 44,   A178242,
%C A181407    3, 11, 17, 12, 16, 41, 51, 31, 37,  87, 101, 58,
%C A181407    8  23, 31, 20, 25, 61, 73, 43, 50, 115, 131, 74,
%C A181407   15, 39, 49, 30, 36, 85, 99, 57, 65, 147, 165, 92.
%C A181407 Columns are (or from) A005563, A142463, A056220, A002378, A000290, A001844, A058331, A002061, A002522, A097080, A093328, A014206.
%H A181407 G. C. Greubel, <a href="/A181407/b181407.txt">Table of n, a(n) for n = 0..1000</a>
%H A181407 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (6,-12,8).
%F A181407 a(n) = 16*A001788(n-4).
%F A181407 a(n+1) - a(n) = A178987(n).
%F A181407 G.f.: (3 - 15*x + 20*x^2) / (1-2*x)^3. - _R. J. Mathar_, Jan 30 2011
%F A181407 E.g.f.: (x^2 - 3*x + 3)*exp(2*x). - _G. C. Greubel_, Feb 21 2019
%t A181407 Table[(n-4)*(n-3)*2^(n-2), {n,0,40}] (* _G. C. Greubel_, Feb 21 2019 *)
%o A181407 (Magma) [(n-4)*(n-3)*2^(n-2): n in [0..40] ]; // _Vincenzo Librandi_, Feb 01 2011
%o A181407 (PARI) vector(40, n, n--; (n-4)*(n-3)*2^(n-2)) \\ _G. C. Greubel_, Feb 21 2019
%o A181407 (Sage) [(n-4)*(n-3)*2^(n-2) for n in (0..40)] # _G. C. Greubel_, Feb 21 2019
%o A181407 (GAP) List([0..40], n-> (n-4)*(n-3)*2^(n-2)); # _G. C. Greubel_, Feb 21 2019
%Y A181407 Cf. A176027, A181318.
%K A181407 nonn,easy
%O A181407 0,1
%A A181407 _Paul Curtz_, Jan 28 2011