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A137454
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A triangular sequence from coefficients of a three deep quadratic polynomial recursion: p(x,n)=x^2*p(x,n-1)+(-x-1)*p(x,n-2)+p(x,n-3).
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0
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1, -1, -1, 1, -1, -1, -1, -1, 1, 2, 2, -1, -2, -1, -1, 1, 0, 1, 5, 4, -1, -3, -1, -1, 1, -3, -5, -2, 3, 9, 6, -1, -4, -1, -1, 1, 2, 1, -10, -16, -6, 6, 14, 8, -1, -5, -1, -1, 1, 3, 9, 14, 4, -23, -34, -12, 10, 20, 10, -1, -6, -1, -1, 1, -5, -8, 10, 38, 45, 10, -44, -60, -20, 15, 27, 12, -1, -7, -1, -1, 1, -1, -11, -38, -42, 23, 101, 105, 20
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OFFSET
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1,10
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COMMENTS
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Row sums are r() = 1, -1, -3, 0, 5, 2, -8, -7, 11, 17, -12, -35, 6, 64, 17, -105, -75, 152, 197, -182, -424... with r(n)=r(n-1)-2*r(n-2)+r(n-3).
The row sums appear to be a saw tooth alternating sequence.
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LINKS
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Table of n, a(n) for n=1..89.
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FORMULA
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p(x,-1)=0;p(x,0)=1;p(x,1)=x^2-x-2; p(x,n)=x^2*p(x,n-1)+(-x-1)*p(x,n-2)+p(x,n-3).
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EXAMPLE
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{1},
{-1, -1, 1},
{-1, -1, -1, -1, 1},
{2, 2, -1, -2, -1, -1, 1},
{0, 1, 5, 4, -1, -3, -1, -1, 1},
{-3, -5, -2, 3,9, 6, -1, -4, -1, -1, 1},
{2, 1, -10, -16, -6, 6,14, 8, -1, -5, -1, -1, 1},
{3, 9,14, 4, -23, -34, -12, 10, 20, 10, -1, -6, -1, -1, 1},
{-5, -8, 10, 38, 45, 10, -44, -60, -20, 15,27, 12, -1, -7, -1, -1, 1},
{-1, -11, -38, -42, 23, 101, 105,20, -75, -95, -30, 21, 35, 14, -1, -8, -1, -1,1},
{8, 22, 11, -55, -144, -131, 45, 215, 205, 35, -118, -140, -42, 28, 44, 16, -1, -9, -1, -1, 1}
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MATHEMATICA
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Clear[A, x, p] p[x, -1] = 0; p[x, 0] = 1; p[x, 1] = x^2 - x - 1; p[x_, n_] := x^2*p[x, n - 1] + (-x - 1)*p[x, n - 2] + p[x, n - 3]; Table[Expand[p[x, n]], {n, 0, 10}]; a1 = Table[CoefficientList[p[x, n], x], {n, 0, 10}]; Flatten[a1]
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CROSSREFS
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Cf. A084610.
Sequence in context: A221649 A090406 A152723 * A030613 A092984 A086600
Adjacent sequences: A137451 A137452 A137453 * A137455 A137456 A137457
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KEYWORD
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tabf,uned,sign
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AUTHOR
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Roger L. Bagula and Gary W. Adamson, Apr 18 2008
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STATUS
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approved
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