A396313 Number of tilings of a 5 X n rectangle by unit squares and the Ferrers tile (3,3,2).

1, 1, 1, 4, 7, 11, 24, 46, 83, 162, 311, 584, 1116, 2132, 4046, 7705, 14685, 27939, 53186, 101287, 192809, 367052, 698852, 1330465, 2532908, 4822273, 9180720, 17478296, 33275580, 63350648, 120607809, 229615269, 437145509, 832244516, 1584440971, 3016485307

Offset

0,4

Comments

The Ferrers tile (3,3,2) has three columns of heights 3, 3, and 2.

Links

Table of n, a(n) for n=0..35.

Per Alexandersson and John Ahlberg, Polynomials from tilings of rectangles, arXiv:2605.03473 [math.CO], 2026.

Index entries for linear recurrences with constant coefficients, signature (1,0,3,0,1).

Formula

G.f.: 1/(1 - x - 3*x^3 - x^5).

With a(0)=1, a(n) = a(n-1) + 3*a(n-3) + a(n-5) for n >= 1.

Mathematica

CoefficientList[Series[1/(1 - x - 3*x^3 - x^5), {x, 0, 35}], x] (* Stefano Spezia, May 21 2026 *)

Crossrefs

Cf. A396311, A396312.

Sequence in context: A288111 A352214 A375315 * A179165 A369546 A128836

Adjacent sequences: A396310 A396311 A396312 * A396317 A396318 A396320

Keyword

nonn,easy

Author

Per Alexandersson, May 21 2026

Status

approved