A336732 The number of tight 4 X n pavings.

0, 1, 26, 282, 2072, 12279, 63858, 305464, 1382648, 6029325, 25628762, 107026662, 441439944, 1804904755, 7334032754, 29669499492, 119647095176, 481400350185, 1933747745850, 7758556171570, 31102292517560, 124605486285231, 498987240470066, 1997573938402512

Offset: 0

Author

Roberto Tauraso, Aug 02 2020

Keywords

• nonn
• easy

Comments

This is row (or column) m=4 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 (18,-139,604,-1627,2818,-3141,2176,-852,144).

Crossrefs

Cf. A000295 (m=2), A285357, A285361 (m=3), A336734 (m=5).

Programs

Maple

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);

Mathematica

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]

Formula

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.

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)).