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A192752
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Constant term of the reduction by x^2->x+1 of the polynomial p(n,x) defined below in Comments.
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3
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1, 7, 12, 23, 39, 66, 109, 179, 292, 475, 771, 1250, 2025, 3279, 5308, 8591, 13903, 22498, 36405, 58907, 95316, 154227, 249547, 403778, 653329, 1057111, 1710444, 2767559, 4478007, 7245570, 11723581, 18969155, 30692740, 49661899, 80354643
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OFFSET
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0,2
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COMMENTS
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The titular polynomial is defined recursively by p(n,x)=x*(n-1,x)+4n+3 for n>0, where p(0,x)=1. For discussions of polynomial reduction, see A192232 and A192744.
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LINKS
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Table of n, a(n) for n=0..34.
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FORMULA
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Conjecture: G.f.: ( 1+5*x-2*x^2 ) / ( (x-1)*(x^2+x-1) ). a(n) = A000071(n+3)+5*A000071(n+2) -2*A000071(n+1) and first differences in A022136. - R. J. Mathar, May 04 2014
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MATHEMATICA
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q = x^2; s = x + 1; z = 40;
p[0, n_] := 1; p[n_, x_] := x*p[n - 1, x] + 4 n + 3;
Table[Expand[p[n, x]], {n, 0, 7}]
reduce[{p1_, q_, s_, x_}] :=
FixedPoint[(s PolynomialQuotient @@ #1 +
PolynomialRemainder @@ #1 &)[{#1, q, x}] &, p1]
t = Table[reduce[{p[n, x], q, s, x}], {n, 0, z}];
u1 = Table[Coefficient[Part[t, n], x, 0], {n, 1, z}](* A192752 *)
u2 = Table[Coefficient[Part[t, n], x, 1], {n, 1, z}](* A192753 *)
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CROSSREFS
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Cf. A192744, A192232, A192753.
Sequence in context: A273178 A160423 A252652 * A097925 A132195 A076852
Adjacent sequences: A192749 A192750 A192751 * A192753 A192754 A192755
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KEYWORD
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nonn
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AUTHOR
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Clark Kimberling, Jul 09 2011
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STATUS
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approved
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