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A358035
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a(n) = (8*n^3 + 12*n^2 + 4*n - 9)/3.
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1
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5, 37, 109, 237, 437, 725, 1117, 1629, 2277, 3077, 4045, 5197, 6549, 8117, 9917, 11965, 14277, 16869, 19757, 22957, 26485, 30357, 34589, 39197, 44197, 49605, 55437, 61709, 68437, 75637, 83325, 91517, 100229, 109477, 119277, 129645, 140597, 152149, 164317
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OFFSET
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1,1
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COMMENTS
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Conjecture: a(n) is the disorder number of the Aztec diamond of size n.
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REFERENCES
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G. E. Andrews and K. Eriksson, Integer Partitions, Cambridge University Press, 2004.
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LINKS
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FORMULA
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G.f.: x*(5 + 17*x - 9*x^2 + 3*x^3)/(1 - x)^4. - Stefano Spezia, Oct 26 2022
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MATHEMATICA
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Table[(8n^3+12n^2+4n-9)/3, {n, 40}] (* or *) LinearRecurrence[{4, -6, 4, -1}, {5, 37, 109, 237}, 40] (* Harvey P. Dale, Nov 20 2022 *)
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PROG
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(Python)
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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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