A396312 Number of tilings of an (h+3) X n rectangle by unit squares and the Ferrers tile (h,2,2,1), for h >= 4.

1, 1, 1, 1, 5, 12, 22, 38, 72, 148, 301, 593, 1149, 2242, 4423, 8743, 17218, 33815, 66436, 130699, 257247, 506154, 995529, 1957987, 3851477, 7576734, 14904863, 29319295, 57673054, 113448372, 223166548, 438995465, 863552302, 1698697632, 3341519128, 6573134853

Offset

0,5

Comments

The sequence is independent of h for h >= 4.

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 (1,0,0,4,3,3,6,2,2,4,0,0,1).

Formula

G.f.: 1/(1 - x - 4*x^4 - 3*x^5 - 3*x^6 - 6*x^7 - 2*x^8 - 2*x^9 - 4*x^10 - x^13).

With a(0)=1, a(n) = a(n-1) + 4*a(n-4) + 3*a(n-5) + 3*a(n-6) + 6*a(n-7) + 2*a(n-8) + 2*a(n-9) + 4*a(n-10) + a(n-13) for n >= 1.

Mathematica

CoefficientList[Series[1/(1 - x - 4*x^4 - 3*x^5 - 3*x^6 - 6*x^7 - 2*x^8 - 2*x^9 - 4*x^10 - x^13), {x, 0, 35}], x] (* Stefano Spezia, May 21 2026 *)

Crossrefs

Cf. A396311, A396313.

Sequence in context: A225247 A299257 A298791 * A054307 A172295 A332569

Adjacent sequences: A396309 A396310 A396311 * A396313 A396317 A396318

Keyword

nonn,easy

Author

Per Alexandersson, May 21 2026

Status

approved