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A050400
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Number of independent sets of vertices in P_3 X C_n (n > 2).
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2
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5, 1, 17, 43, 181, 621, 2309, 8303, 30277, 109753, 398857, 1447931, 5258725, 19095285, 69344061, 251811903, 914429445, 3320635025, 12058502657, 43789003563, 159014593621, 577442573597, 2096914206261, 7614694850543, 27651860345029, 100414447219721, 364643142303353
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OFFSET
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0,1
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LINKS
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FORMULA
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a(n) = a(n-1) + 8*a(n-2) + 6*a(n-3) - a(n-4) - a(n-5).
G.f.: (5-4*x-24*x^2-12*x^3+x^4)/((1+x)*(1-2*x-6*x^2+x^4)). - Maksym Voznyy (voznyy(AT)mail.ru), Aug 12 2009
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MAPLE
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seq(coeff(series((5-4*x-24*x^2-12*x^3+x^4)/((1+x)*(1-2*x-6*x^2+x^4)), x, n+1), x, n), n = 0..30); # G. C. Greubel, Oct 30 2019
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MATHEMATICA
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CoefficientList[Series[(5-4*x-24*x^2-12*x^3+x^4)/((1+x)*(1-2*x-6*x^2+ x^4)), {x, 0, 30}], x] (* Vincenzo Librandi, May 11 2017 *)
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PROG
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(Magma) I:=[5, 1, 17, 43, 181]; [n le 5 select I[n] else Self(n-1) + 8*Self(n-2) + 6*Self(n-3) - Self(n-4) - Self(n-5): n in [1..30]]; // Vincenzo Librandi, May 11 2017
(PARI) my(x='x+O('x^30)); Vec((5-4*x-24*x^2-12*x^3+x^4)/((1+x)*(1-2*x-6*x^2+x^4))) \\ G. C. Greubel, Oct 30 2019
(Sage)
P.<x> = PowerSeriesRing(ZZ, prec)
return P((5-4*x-24*x^2-12*x^3+x^4)/((1+x)*(1-2*x-6*x^2+x^4))).list()
(GAP) a:=[5, 1, 17, 43, 181];; for n in [6..30] do a[n]:=a[n-1]+8*a[n-2] +6*a[n-3] -a[n-4]-a[n-5]; od; a; # G. C. Greubel, Oct 30 2019
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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EXTENSIONS
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More terms from Michael Lugo (mlugo(AT)thelabelguy.com), Dec 22 1999
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STATUS
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approved
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