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