|
%I #38 Mar 09 2024 14:51:14
%S 1,4,13,36,93,228,541,1252,2845,6372,14109,30948,67357,145636,313117,
%T 669924,1427229,3029220,6407965,13514980,28428061,59652324,124897053,
%U 260978916,544327453,1133394148,2356266781,4891490532,10140895005,20997617892,43426891549
%N a(n) = ((3*n + 1)*2^(n+3) + 9 + (-1)^n)/18.
%C A floretion-generated sequence resulting from particular transform of A000975.
%C Floretion Algebra Multiplication Program, FAMP Code: 2jesforseq[ + .5'i + 'kk' + .5'jk' ], 1vesforseq(n) = A000975(n+2)*(-1)^(n+1), ForType: 1A, LoopType: tes (2nd iteration)
%H G. C. Greubel, <a href="/A102301/b102301.txt">Table of n, a(n) for n = 0..1000</a>
%H T. Etzion, <a href="http://dx.doi.org/10.1109/TIT.2006.883542">On the stopping redundancy of Reed-Muller codes</a>, IEEE Trans. Information Theory 52 (11) (2006) 4867-4879, <a href="https://arxiv.org/abs/cs/0511056">also</a>, arXiv:cs/0511056 [cs.IT], 2005.
%H Toufik Mansour and Armend Sh. Shabani, <a href="https://doi.org/10.3906/mat-1803-113">Bargraphs in bargraphs</a>, Turkish Journal of Mathematics (2018) Vol. 42, Issue 5, 2763-2773.
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-3,-4,4).
%F G.f.: 1/((1-x^2)*(1-2*x)^2).
%F a(n+1) - 2*a(n) = A000975(n+2) (n-th number without consecutive equal binary digits)
%F a(n) + a(n+1) = A000337(n+2);
%F a(n+1) - a(n) = A045883(n+2);
%F a(n+2) - a(n) = A001787(n+3) ( Number of edges in n-dimensional hypercube );
%F a(n+2) - 2*a(n+1) + a(n) = A059570(n+3);
%F Convolution of "Number of fixed points in all 231-avoiding involutions in S_n" (A059570) with the natural numbers (A000027), treating the result as if offset=0. - _Graeme McRae_, Jul 12 2006
%F Equals triangle A059260 * A008574 as a vector, where A008574 = [1, 4, 8, 12, 16, 20, ...]. - _Gary W. Adamson_, Mar 06 2012
%t Table[((3n+1)*2^(n+3) + 9 + (-1)^n)/18, {n,0,50}] (* _G. C. Greubel_, Sep 27 2017 *)
%t LinearRecurrence[{4, -3, -4, 4}, {1, 4, 13, 36}, 50] (* _Vincenzo Librandi_, Nov 21 2018 *)
%o (PARI) a(n)=((3*n+1)*2^(n+3)+9+(-1)^n)/18 \\ _Charles R Greathouse IV_, Oct 16 2015
%o (Magma) [((3*n+1)*2^(n+3)+9+(-1)^n)/18: n in [0..40]]; // _Vincenzo Librandi_, Nov 21 2018
%Y Cf. A000975, A000337, A045883, A001787, A059570, A137266, A008574, A059260.
%K easy,nonn
%O 0,2
%A _Creighton Dement_, Feb 20 2005
|
