|
%I #16 Aug 02 2020 09:46:21
%S 0,1,26,282,2072,12279,63858,305464,1382648,6029325,25628762,
%T 107026662,441439944,1804904755,7334032754,29669499492,119647095176,
%U 481400350185,1933747745850,7758556171570,31102292517560,124605486285231,498987240470066,1997573938402512
%N The number of tight 4 X n pavings.
%C This is row (or column) m=4 of the array T in A285357.
%H D. E. Knuth (Proposer), <a href="http://dx.doi.org/10.4169/amer.math.monthly.124.8.754">Problem 12005</a>, Amer. Math. Monthly 124 (No. 8, Oct. 2017), page 755. For the <a href="https://doi.org/10.1080/00029890.2019.1621132">solution</a> see op. cit., 126 (No. 7, 2019), 660-664.
%H Roberto Tauraso, <a href="http://www.mat.uniroma2.it/~tauraso/AMM/AMM12005.pdf">Problem 12005, Proposed solution</a>.
%H <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (18,-139,604,-1627,2818,-3141,2176,-852,144).
%F a(n) = (4^(n+5)+(n-42)*3^(n+4)-9*(2*n-27)*2^(n+5)-36*n^3-486*n^2-2577*n-5398)/36.
%F G.f.: (x+8*x^2-47*x^3+6*x^4+104*x^5)/((1-x)^4*(1-2*x)^2*(1-3*x)^2*(1-4*x)).
%p seq((4^(n+5)+(n-42)*3^(n+4)-9*(2*n-27)*2^(n+5)-36*n^3-486*n^2-2577*n-5398)/36,n=0..20);
%t num=(x+8*x^2-47*x^3+6*x^4+104*x^5); den=((1-x)^4*(1-2*x)^2*(1-3*x)^2*(1-4*x)); CoefficientList[Series[num/den,{x,0,20}],x]
%Y Cf. A000295 (m=2), A285357, A285361 (m=3), A336734 (m=5).
%K nonn,easy
%O 0,3
%A _Roberto Tauraso_, Aug 02 2020
|
