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A192469
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Coefficient of x in the reduction by x^2->x+3 of the polynomial p(n,x)=1+x^n+x^(2n).
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3
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2, 8, 44, 224, 1178, 6200, 32786, 173600, 919988, 4877072, 25858754, 137115440, 727074530, 3855471416, 20444603516, 108412922240, 574888887530, 3048505597160, 16165538467442, 85722217226576, 454565670533252, 2410459729834544
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OFFSET
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1,1
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COMMENTS
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For an introduction to reductions of polynomials by substitutions such as x^2->x+3, see A192232.
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LINKS
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Table of n, a(n) for n=1..22.
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FORMULA
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Empirical G.f.: -2*x*(x-1)*(3*x-1)/((3*x^2+x-1)*(9*x^2-7*x+1)). [Colin Barker, Nov 12 2012]
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EXAMPLE
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The first four polynomials p(n,x) and their reductions are as follows:
p(1,x)=1+x+x^2 -> 4+2x
p(2,x)=1+x^2+x^4 -> 16+8x
p(3,x)=1+x^3+x^6 -> 61+44x
p(4,x)=1+x^4+x^8 -> 304+224x.
From these, read
A192468=(4,16,61,304,...) and A192469=(2,8,44,224,...)
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MATHEMATICA
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(See A192468.)
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CROSSREFS
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Cf. A192232, A192468.
Sequence in context: A264565 A018985 A018986 * A128656 A208044 A291697
Adjacent sequences: A192466 A192467 A192468 * A192470 A192471 A192472
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KEYWORD
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nonn
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AUTHOR
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Clark Kimberling, Jul 01 2011
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STATUS
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approved
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