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A027053
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a(n) = T(n,n+2), T given by A027052.
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6
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1, 4, 9, 18, 35, 66, 123, 228, 421, 776, 1429, 2630, 4839, 8902, 16375, 30120, 55401, 101900, 187425, 344730, 634059, 1166218, 2145011, 3945292, 7256525, 13346832, 24548653, 45152014, 83047503, 152748174, 280947695, 516743376
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OFFSET
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2,2
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COMMENTS
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Second differences of (A027026(n)-1)/2.
a(n) is also the number of fixed polyominoes with n cells of height (or width) 2. - David Bevan, Sep 09 2009
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LINKS
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FORMULA
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G.f.: x^2*(1+x)^2/((1-x)*(1-x-x^2-x^3)).
a(n) = a(n-1) + a(n-2) + a(n-3) + 4. - David Bevan, Sep 09 2009
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MAPLE
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seq(coeff(series(x^2*(1+x)^2/((1-x)*(1-x-x^2-x^3)), x, n+1), x, n), n = 2 ..30); # G. C. Greubel, Nov 05 2019
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MATHEMATICA
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LinearRecurrence[{2, 0, 0, -1}, {1, 4, 9, 18}, 30] (* G. C. Greubel, Nov 05 2019 *)
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PROG
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(PARI) my(x='x+O('x^32)); Vec(x^2*(1+x)^2/((1-x)*(1-x-x^2-x^3))) \\ G. C. Greubel, Nov 05 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 32); Coefficients(R!( x^2*(1+x)^2/((1-x)*(1-x-x^2-x^3)) )); // G. C. Greubel, Nov 05 2019
(Sage)
P.<x> = PowerSeriesRing(ZZ, prec)
return P(x^2*(1+x)^2/((1-x)*(1-x-x^2-x^3))).list()
(GAP) a:=[1, 4, 9, 18];; for n in [5..30] do a[n]:=2*a[n-1]-a[n-4]; od; a; # G. C. Greubel, Nov 05 2019
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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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