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The number of tight 5 X n pavings.
4

%I #13 Aug 03 2020 00:55:32

%S 0,1,57,1071,12279,106738,781458,5111986,30980370,178047831,985621119,

%T 5311715977,28075774881,146309927344,754544640000,3861338821620,

%U 19646614600164,99532074868285,502608221035605,2531829420822835,12730273358124315,63919766245452606

%N The number of tight 5 X n pavings.

%C This is row (or column) m=5 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_13">Index entries for linear recurrences with constant coefficients</a>, signature (31,-432,3580,-19666,75558,-208736,419600,-613605,644771,-473432,230220,-66528,8640).

%F a(n) = (5^(n+7)+(2*n-66)*4^(n+6)+(16*n^2-1432*n+13164)*3^(n+3) +(303*n-1505)*2^(n+10)+576*n^4+13248*n^3+129936*n^2+646972*n+1377903)/576.

%F G.f.: (x +26*x^2 -264*x^3 +122*x^4 +4367*x^5 -11668*x^6 +3000*x^7 +11168*x^8 +160*x^9) / ((1-x)^5*(1-2*x)^2*(1-3*x)^3*(1-4*x)^2*(1-5*x)).

%Y Cf. A000295 (m=2), A285357, A285361 (m=3), A336732 (m=4).

%K nonn,easy

%O 0,3

%A _Roberto Tauraso_, Aug 02 2020