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%I #14 Feb 09 2021 02:41:12
%S 1,1,1,1,1,1,1,1,1,1,6,6,11,11,21,26,41,56,86,121,181,256,381,541,801,
%T 1146,1686,2426,3551,5131,7486,10841,15791,22896,33321,48346,70321,
%U 102076,148416,215506,313256,454961,661206,960446,1395686,2027501
%N a(n) = a(n-2) + a(n-4) + a(n-5) + a(n-7) + a(n-8) + a(n-10) for n >= 10, with a(0) = ... = a(9) = 1.
%C Shannon mentions this recurrence with characteristic polynomial x^10 +x^8 +x^7 +x^5 +x^4 +x^2 -1 = 0 in connection with the channel capacity Cp = Log[W] = Log[xroot_max] = 0.539... .
%D Claude Shannon and Warren Weaver, A Mathematical Theory of Communication, University of Illinois Press, Chicago, 1963, pages 37-38.
%H G. C. Greubel, <a href="/A122762/b122762.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (0,1,0,1,1,0,1,1,0,1).
%F O.g.f.: (1 +x -x^4 -2*x^5 -2*x^6 -3*x^7 -4*x^8 -4*x^9)/(1 -x^2 -x^4 -x^5 -x^7 -x^8 -x^10). - _R. J. Mathar_, Dec 05 2007
%t a[n_]:= a[n]= If[n<10, 1, a[n-2] +a[n-4] +a[n-5] +a[n-7] +a[n-8] +a[n-10]];
%t Table[a[n], {n, 0, 50}]
%o (Sage)
%o def A122762_list(prec):
%o P.<x> = PowerSeriesRing(ZZ, prec)
%o return P( (1+x-x^4-2*x^5-2*x^6-3*x^7-4*x^8-4*x^9)/(1-x^2-x^4-x^5-x^7-x^8 -x^10) ).list()
%o A122762_list(50) # _G. C. Greubel_, Feb 08 2021
%o (Magma)
%o R<x>:=PowerSeriesRing(Rationals(), 50);
%o Coefficients(R!( (1+x-x^4-2*x^5-2*x^6-3*x^7-4*x^8-4*x^9)/(1-x^2-x^4-x^5-x^7-x^8 -x^10) )); // _G. C. Greubel_, Feb 08 2021
%Y Cf. A143351, A143372, A143373, A143375.
%K nonn
%O 0,11
%A _Roger L. Bagula_, Sep 21 2006
%E Edited by _N. J. A. Sloane_, May 09 2007
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