A336734 The number of tight 5 X n pavings.

0, 1, 57, 1071, 12279, 106738, 781458, 5111986, 30980370, 178047831, 985621119, 5311715977, 28075774881, 146309927344, 754544640000, 3861338821620, 19646614600164, 99532074868285, 502608221035605, 2531829420822835, 12730273358124315, 63919766245452606

Offset: 0

Author

Roberto Tauraso, Aug 02 2020

Keywords

• nonn
• easy

Comments

This is row (or column) m=5 of the array T in A285357.

Links

• D. E. Knuth (Proposer), Problem 12005, Amer. Math. Monthly 124 (No. 8, Oct. 2017), page 755. For the solution see op. cit., 126 (No. 7, 2019), 660-664.
• Roberto Tauraso, Problem 12005, Proposed solution.
• Index entries for linear recurrences with constant coefficients, signature (31,-432,3580,-19666,75558,-208736,419600,-613605,644771,-473432,230220,-66528,8640).

Crossrefs

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

Formula

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.

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)).