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A345897
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a(n) = 2*n^4/3 - 4*n^3/3 + 11*n^2/6 - 13*n/6 + 1.
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1
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1, 0, 4, 29, 107, 286, 630, 1219, 2149, 3532, 5496, 8185, 11759, 16394, 22282, 29631, 38665, 49624, 62764, 78357, 96691, 118070, 142814, 171259, 203757, 240676, 282400, 329329, 381879, 440482, 505586, 577655, 657169, 744624, 840532, 945421, 1059835, 1184334, 1319494
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OFFSET
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0,3
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COMMENTS
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For n >=1, a(n) is the number of divisions of a 2 X n board into 3 pieces. See Jacob Brown article.
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LINKS
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FORMULA
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a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n > 4.
G.f.: (1 - 5*x + 14*x^2 - x^3 + 7*x^4)/(1-x)^5. (End)
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MATHEMATICA
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CoefficientList[Series[(1 - 5 x + 14 x^2 - x^3 + 7 x^4)/(1 - x)^5, {x, 0, 38}], x] (* Michael De Vlieger, Apr 28 2023 *)
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PROG
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(PARI) a(n) = 2*n^4/3 - 4*n^3/3 + 11*n^2/6 - 13*n/6 + 1;
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CROSSREFS
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Cf. A172482 (same but where the rightmost squares separate).
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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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