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Search: id:A136487
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| A136487 |
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Coefficents of designed "null" term polynomial recursion: the cubic term is zero: p(x,n)=(x+1)*p(x,n-1)-(x^2-1)*p(x,n-2). |
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+0
1
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| 1, 1, 1, 1, 1, -1, -1, -1, 0, 2, 0, -1, 2, 0, -4, 0, 2, -3, 2, 7, -4, -5, 2, 1, 5, -5, -11, 11, 7, -7, -1, 1, -8, 12, 16, -28, -8, 20, 0, -4, 13, -25, -20, 60, -2, -46, 12, 12, -3, -1, -21, 50, 19, -120, 38, 92, -50, -24, 15, 2, -1
(list; graph; listen)
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OFFSET
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1,10
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COMMENT
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Row sums are:
1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0}
A converse recursion is with different signs but same absolute coefficients is:
P[x, -1] = 0; P[x, 0] = 1; P[x, 1] = x - 1;
P[x_, n_] := P[x, n] = (x + 1)*P[x, n - 1] - (x^2 - 1)*P[x, n - 2]
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FORMULA
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p(x,-1)=0;p(x,0)=1;p(x,1)=x+1; p(x,n)=(x+1)*p(x,n-1)-(x^2-1)*p(x,n-2)
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EXAMPLE
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{1},
{1, 1},
{}, <- designed null tern
{1, 1, -1, -1},
{-1, 0, 2, 0, -1},
{2, 0, -4, 0, 2},
{-3, 2, 7, -4, -5, 2, 1},
{5, -5, -11, 11, 7, -7, -1, 1},
{-8, 12, 16, -28, -8, 20, 0, -4},
{13, -25, -20, 60, -2, -46, 12, 12, -3, -1},
{-21, 50, 19, -120, 38, 92, -50, -24, 15, 2, -1}
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MATHEMATICA
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Clear[P, n, m, x] P[x, -1]=0; P[x, 0]=1; P[x, 1]=x-1; P[x_, n_]:=P[x, n]=(x+1)*P[x, n-1]-(x^2-1)*P[x, n-2]; a=Table[CoefficientList[P[x, n], x], {n, 0, 10}]; Flatten[a]
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CROSSREFS
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Adjacent sequences: A136484 A136485 A136486 this_sequence A136488 A136489 A136490
Sequence in context: A025679 A071491 A137298 this_sequence A021501 A101662 A091064
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KEYWORD
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uned,tabf,sign
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Mar 21 2008
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