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A051360
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A class of Boolean functions of n variables and rank 4.
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1
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0, 0, 0, 16, 389, 3112, 16231, 66177, 228438, 697219, 1932601, 4953493, 11892484, 27003029, 58421782, 121154728, 241995312, 467422242, 875997590, 1597434614, 2841382379, 4940146414, 8411111897, 14046656347, 23041951126, 37174397565, 59052693975, 92458885395
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OFFSET
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0,4
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REFERENCES
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V. Jovovic, G. Kilibarda, On the number of Boolean functions in the Post classes F^{mu}_8, Diskretnaya Matematika, 11 (1999), no. 4, 127-138 (translated in Discrete Mathematics and Applications, 9, (1999), no. 6).
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (16,-120,560,-1820,4368,-8008,11440,-12870,11440,-8008,4368,-1820,560,-120,16,-1).
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FORMULA
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a(n) = n*(n-1)*(n-2)*(n^12 + 123*n^11 + 6947*n^10 + 238995*n^9 + 5406153*n^8 + 81325989*n^7 + 826126601*n^6 + 6015252225*n^5 + 31515483346*n^4 + 95237254188*n^3 + 64213530552*n^2-798617063520*n-2101517913600)/15!.
G.f.: -x^3*(6*x^12 -84*x^11 +535*x^10 -2058*x^9 +5335*x^8 -9813*x^7 +13093*x^6 -12698*x^5 +8799*x^4 -4159*x^3 +1192*x^2 -133*x -16) / (x -1)^16. - Colin Barker, Jul 11 2013
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MATHEMATICA
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CoefficientList[Series[-x^3*(6*x^12 -84*x^11 +535*x^10 -2058*x^9 +5335*x^8 -9813*x^7 +13093*x^6 -12698*x^5 +8799*x^4 -4159*x^3 +1192*x^2 -133*x -16) / (x -1)^16, {x, 0, 50}], x] (* G. C. Greubel, Oct 07 2017 *)
LinearRecurrence[{16, -120, 560, -1820, 4368, -8008, 11440, -12870, 11440, -8008, 4368, -1820, 560, -120, 16, -1}, {0, 0, 0, 16, 389, 3112, 16231, 66177, 228438, 697219, 1932601, 4953493, 11892484, 27003029, 58421782, 121154728}, 40] (* Harvey P. Dale, Sep 04 2021 *)
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PROG
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(PARI) x='x+O('x^50); concat([0, 0, 0], Vec(-x^3*(6*x^12 -84*x^11 +535*x^10 -2058*x^9 +5335*x^8 -9813*x^7 +13093*x^6 -12698*x^5 +8799*x^4 -4159*x^3 +1192*x^2 -133*x -16)/(x -1)^16)) \\ G. C. Greubel, Oct 07 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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