A352590 Number of tilings of a 4 X n rectangle using 2 X 2 and 1 X 1 tiles and dominoes.

1, 5, 90, 1125, 15623, 210690, 2865581, 38879777, 527889422, 7165926641, 97281018915, 1320614646178, 17927775213129, 243375024977525, 3303891838175262, 44851355548842869, 608871075513683799, 8265613771134660506, 112208272012556064101, 1523262112532452904985

Offset

0,2

Comments

The sequence is based on A352589.

Links

Table of n, a(n) for n=0..19.

Index entries for linear recurrences with constant coefficients, signature (11,50,-189,-289,1164,-408,-1010,576,216,-120).

Formula

G.f.: (1-6*x-15*x^2+74*x^3-18*x^4-122*x^5+64*x^6+48*x^7-24*x^8) / (1-11*x-50*x^2+189*x^3+289*x^4-1164*x^5+408*x^6+1010*x^7-576*x^8-216*x^9+120*x^10).

Recurrence: a(n)=11*a(n-1) + 50*a(n-2) - 189*a(n-3) - 289*a(n-4) + 1164*a(n-5) - 408*a(n-6) - 1010*a(n-7) + 576*a(n-8) + 216*a(n-9) - 120*a(n-10).

Mathematica

CoefficientList[Series[(1-6x-15x^2+74x^3-18x^4-122x^5+64x^6+48x^7-24x^8)/(1-11x-50x^2+189x^3+289x^4-1164x^5+408x^6+1010x^7-576x^8-216x^9+120x^10), {x, 0, 20}], x] (* or *) LinearRecurrence[{11, 50, -189, -289, 1164, -408, -1010, 576, 216, -120}, {1, 5, 90, 1125, 15623, 210690, 2865581, 38879777, 527889422, 7165926641}, 30] (* Harvey P. Dale, Feb 27 2023 *)

Crossrefs

Cf. A352589, A352591.

Sequence in context: A300767 A300637 A301359 * A037297 A277303 A361551

Adjacent sequences: A352587 A352588 A352589 * A352591 A352592 A352593

Keyword

nonn,easy

Author

Gerhard Kirchner, Mar 22 2022

Status

approved