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A355883
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Number of ways to 5-color a 3 X n grid ignoring the variations of two colors.
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2
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4, 169, 7141, 301741, 12749989, 538747549, 22764640981, 961914128461, 40645437426949, 1717462645311229, 72570948297479221, 3066467006530462381, 129572785291363217509, 5475065165353811151709, 231347489347123368595861, 9775529461439509493215501
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OFFSET
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1,1
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COMMENTS
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LINKS
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FORMULA
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G.f.: x*(4-11*x)/(1-45*x+116*x^2).
a(n) = 45*a(n-1) - 116*a(n-2) with a(1) = 4, a(2) = 169.
a(n) = 2^(-3-n)*((45 - sqrt(1561))^n*(11*sqrt(1561) - 433) + (45 + sqrt(1561))^n*(11*sqrt(1561) + 433))/(29*sqrt(1561)). - Stefano Spezia, Jul 24 2022
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EXAMPLE
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a(1)=4, 5 colors 1,2,3,4,5: 121, 123, 124, 125.
The first two colors do not vary.
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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