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A265234
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Number of 4 X n arrays containing n copies of 0..4-1 with no equal vertical neighbors and new values introduced sequentially from 0.
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2
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1, 43, 2592, 184740, 14439456, 1196114464, 103142395392, 9160513923648, 832211576040960, 76971887847571968, 7223525356855099392, 686117529041422350336, 65834293657115919826944, 6371837299781950752276480
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OFFSET
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1,2
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LINKS
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FORMULA
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a(n) = coefficient of x^n*y^n*z^n in (1/24)*(2*x^2 + 6*x*y + 6*x^2*y + 2*y^2 + 6*x*y^2 + 2*x^2*y^2 + 6*x*z + 6*x^2*z + 6*y*z + 24*x*y*z + 6*x^2*y*z + 6*y^2*z + 6*x*y^2*z + 2*z^2 + 6*x*z^2 + 2*x^2*z^2 + 6*y*z^2 + 6*x*y*z^2 + 2*y^2*z^2)^n.
Recurrence of order 6 and degree 6: 5*(n + 5)*(832*n^2 + 5785*n + 8460)*(n + 6)^3*a(n + 6) - 4*(n + 5)*(126464*n^5 + 2941016*n^4 + 26840735*n^3 + 119399663*n^2 + 256228730*n + 208319000)*a(n + 5) + 16*(310336*n^6 + 7680621*n^5 + 78610375*n^4 + 426421788*n^3 + 1294537774*n^2 + 2087600280*n + 1398239904)*a(n + 4) + 128*(n + 4)*(1161472*n^5 + 24822356*n^4 + 207271023*n^3 + 841828441*n^2 + 1653171497*n + 1242989235)*a(n + 3) - 768*(n + 3)*(n + 4)*(3709888*n^4 + 58438003*n^3 + 333112832*n^2 + 813878537*n + 716118600)*a(n + 2) + 9216*(n + 2)*(n + 3)*(n + 4)*(1743872*n^3 + 20496944*n^2 + 74692297*n + 84692065)*a(n + 1) - 34836480*(n + 1)*(n + 2)*(n + 3)*(n + 4)*(832*n^2 + 7449*n + 15077)*a(n) = 0. (End)
a(n) ~ 2^(2*n - 19/2) * 3^(3*n + 7/2) / (Pi^(3/2) * n^(3/2)). - Vaclav Kotesovec, Mar 08 2023
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EXAMPLE
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Some solutions for n=4:
0 0 1 2 0 1 0 1 0 1 0 2 0 0 1 2 0 1 1 2
3 3 0 3 2 3 3 2 2 2 3 3 3 3 3 1 3 2 3 1
2 0 1 1 1 0 2 3 1 0 1 1 2 1 0 0 1 0 0 0
1 2 2 3 3 1 0 2 0 3 2 3 3 2 2 1 3 2 3 2
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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