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A212343
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a(n) = (n+1)*(n-2)*(n-3)/2.
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6
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0, 0, 5, 18, 42, 80, 135, 210, 308, 432, 585, 770, 990, 1248, 1547, 1890, 2280, 2720, 3213, 3762, 4370, 5040, 5775, 6578, 7452, 8400, 9425, 10530, 11718, 12992, 14355, 15810, 17360, 19008, 20757, 22610, 24570, 26640, 28823, 31122, 33540, 36080, 38745, 41538, 44462, 47520, 50715, 54050, 57528
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OFFSET
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2,3
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COMMENTS
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Sequence of coefficients of x^1 in marked mesh pattern generating function Q_{n,132}^(0,3,0,0)(x).
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LINKS
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FORMULA
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For n>=4, a(n) = (n-3)*A212342(n-1).
a(n) = 4*a(n-1)-6*a(n-2)+4*a(n-3)-a(n-4) for n>7. - Colin Barker, Jul 10 2015
Sum_{n>=4} 1/a(n) = 23/72.
Sum_{n>=4} (-1)^n/a(n) = 4*log(2)/3 - 55/72. (End)
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MATHEMATICA
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QQ0[t, x] = (1 - (1-4*x*t)^(1/2)) / (2*x*t); QQ1[t, x] = 1/(1 - t*QQ0[t, x]); QQ2[t, x] = (1 + t*(QQ1[t, x] - QQ0[t, x]))/(1 - t*QQ0[t, x]); QQ3[t, x] = (1 + t*(QQ2[t, x] - QQ0[t, x] + t*(QQ1[t, x] - QQ0[t, x])))/(1 - t*QQ0[t, x]); CoefficientList[Coefficient[Simplify[Series[QQ3[t, x], {t, 0, 35}]], x], t] (* Robert Price, Jun 04 2012 *)
LinearRecurrence[{4, -6, 4, -1}, {0, 0, 5, 18}, 60] (* Harvey P. Dale, Mar 15 2018 *)
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PROG
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(PARI) Vec(-x^4*(2*x-5)/(x-1)^4 + O(x^100)) \\ Colin Barker, Jul 10 2015
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CROSSREFS
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Cf. similar sequences of the type m*(m+1)*(m+k)/2 listed in A267370.
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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