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%I #37 Sep 08 2022 08:45:16
%S 1,5,19,61,179,493,1299,3309,8211,19949,47635,112109,260627,599533,
%T 1366547,3089901,6937107,15476205,34331155,75769325,166451731,
%U 364127725,793500179,1723082221,3729512979,8048092653,17319057939
%N a(n) = ((9*n^2 + 33*n + 26)*2^n + (-1)^n)/27.
%C A floretion-generated sequence relating the number of edges and faces in n-dimensional hypercube.
%C Equals A001787, (1, 4, 12, 32, 80, ...) convolved with A001045, the Jacobsthal sequence. - _Gary W. Adamson_, May 23 2009
%C The sum of the sizes of all inversions in compositions of n. - _Arnold Knopfmacher_, Jan 22 2020
%H G. C. Greubel, <a href="/A102841/b102841.txt">Table of n, a(n) for n = 0..1000</a>
%H M. Archibald, A. Blecher, A. Knopfmacher, M. E. Mays, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL23/Archibald/arch3.html">Inversions and Parity in Compositions of Integers</a>, J. Int. Seq., Vol. 23 (2020), Article 20.4.1.
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (5,-6,-4,8).
%F G.f.: 1/((1+x)*(1-2*x)^3).
%F a(n+1) - 2*a(n) = A045883(n+2).
%F a(n) + a(n+1) = A001788(n+2).
%F a(n) = 5*a(n-1) - 6*a(n-2) - 4*a(n-3) + 8*a(n-4). - _Wesley Ivan Hurt_, Jul 03 2020
%t Table[(1/27)*((9 n^2 + 33 n + 26) 2^n + (-1)^n), {n, 0, 50}] (* or *) LinearRecurrence[{5,-6,-4,8}, {1,5,19,61}, 50] (* _G. C. Greubel_, Sep 27 2017 *)
%o (Magma) [((9*n^2 + 33*n + 26)*2^n + (-1)^n)/27 : n in [0..40]]; // _Wesley Ivan Hurt_, Jul 03 2020
%Y Cf. A045883, A001788, A001793, A102301.
%Y Cf. A001787, A001045. - _Gary W. Adamson_, May 23 2009
%K nonn
%O 0,2
%A _Creighton Dement_, Feb 27 2005
%E Corrected by _T. D. Noe_, Nov 08 2006
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