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A163762
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Triangle of coefficients of polynomials H(n,x)=(U^n+L^n)/2+(U^n-L^n)/(2d), where U=x+d, L=x-d, d=(x+4)^(1/2).
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6
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1, 1, 1, 1, 3, 4, 1, 6, 13, 4, 1, 10, 29, 24, 16, 1, 15, 55, 81, 88, 16, 1, 21, 95, 207, 300, 144, 64, 1, 28, 154, 448, 813, 684, 496, 64, 1, 36, 238, 868, 1913, 2352, 2272, 768, 256, 1, 45, 354, 1554, 4077, 6625, 7984, 4704, 2560, 256, 1, 55, 510, 2622, 8061, 16283
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OFFSET
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1,5
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COMMENTS
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H(n,0)=4^Floor(n/2) for n=0,1,2,...
(Column 2)=A000217 (triangular numbers)
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LINKS
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FORMULA
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H(n,x)=2*x*H(n-1,x)-(x^2-x-4)*H(n-2,x), where H(0,x)=1, H(1,x)=x+1.
H(n,x)=(1+1/d)*U^n+(1-1/d)*L^n, where U=x+d, L=x-d, d=(x+4)^(1/2).
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EXAMPLE
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First six rows:
1
1...1
1...3...4
1...6..13...4
1..10..29..24..16
1..15..55..81..88..16
Row 6 represents x^5+15*x^4+55*x^3+81*x^2+88*x+16.
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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