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A289666
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a(n) = number of weakly threshold graphs on n nodes.
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1
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0, 1, 2, 4, 9, 21, 52, 134, 355, 957, 2608, 7154, 19701, 54379, 150302, 415762, 1150609, 3185147, 8818620, 24418128, 67615743, 187239359, 518506932, 1435875288, 3976322869, 11011542937, 30494088494, 84446895364, 233857897749, 647620493541
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OFFSET
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0,3
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LINKS
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FORMULA
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G.f.: -(x^4+x^2+2*x-1)*x/((x^2+x-1)*(x^3-x^2+3*x-1)).
a(n) = 4*a(n-1) - 3*a(n-2) - a(n-3) - a(n-5) for n>5. - Colin Barker, Jul 26 2017
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MATHEMATICA
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a = DifferenceRoot[Function[{a, n}, {a[n] + a[n+2] + 3a[n+3] - 4a[n+4] + a[n+5] == 0, a[0]==0, a[1]==1, a[2]==2, a[3]==4, a[4]==9, a[5]==21}]];
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PROG
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(PARI) concat(0, Vec(x*(1 - 2*x - x^2 - x^4) / ((1 - x - x^2)*(1 - 3*x + x^2 - x^3)) + O(x^30))) \\ Colin Barker, Jul 26 2017
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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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