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A254150
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Number of independent sets in the generalized Aztec diamond E(L_5,L_{2n-1}).
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4
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1, 8, 73, 689, 6556, 62501, 596113, 5686112, 54239137, 517383521, 4935293524, 47077513469, 449070034657, 4283656560248, 40861585458553, 389776618229969, 3718059650555596, 35466384896440661, 338312070235103473, 3227141903559443792, 30783545081553045457
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OFFSET
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0,2
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COMMENTS
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E(L_5,L_{2n-1}) is the graph with vertices {(a,b) : 1<=a<=5, 1<=b<=2n-1, a+b even and edges between (a,b) and (c,d) if and only if |a-b|=|c-d|=1.
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LINKS
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FORMULA
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Empirical g.f.: -(x^2-4*x+1) / (5*x^3-24*x^2+12*x-1). - Colin Barker, Jan 26 2015
The above g.f. is correct. See A331406 for bounds on the order of the recurrence. - Andrew Howroyd, Jan 16 2020
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PROG
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(PARI) Vec((1 - 4*x + x^2)/(1 - 12*x + 24*x^2 - 5*x^3) + O(x^25)) \\ Andrew Howroyd, Jan 16 2020
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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