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A094184
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Triangle read by rows in which each term equals the entry above minus the entry left plus twice the entry left-above.
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0
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1, 1, 1, 1, 2, 0, 1, 3, 1, -1, 1, 4, 3, -2, 0, 1, 5, 6, -2, -2, 2, 1, 6, 10, 0, -6, 4, 0, 1, 7, 15, 5, -11, 3, 5, -5, 1, 8, 21, 14, -15, -4, 15, -10, 0, 1, 9, 28, 28, -15, -19, 26, -6, -14, 14, 1, 10, 36, 48, -7, -42, 30, 16, -42, 28, 0, 1, 11, 45, 75, 14, -70, 16, 60, -70, 14, 42, -42, 1, 12, 55, 110, 54, -96, -28, 120, -70, -56, 126, -84, 0, 1
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,5
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COMMENTS
| Row sums are A086990 or A090412. (Superseeker finds that the j-th coefficient of OGF(A090412)(z)*(1-z)^j equals A049122). Same absolute values as A065432. Even rows end in 0, odd rows end in Catalan numbers (A000118) with alternating sign.
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FORMULA
| T(i, j)=T(i-1, j)-T(i, j-1)+2*T(i-1, j-1), with T(i, 0)=1 and T(i, j)=0 if j>i.
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EXAMPLE
| Table starts {1},{1,1},{1,2,0},{1,3,1,-1},{1,4,3,-2,0},{1,5,6,-2,-2,2}
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MATHEMATICA
| T[_, 0]:=1; T[0, 0]:=1; T[i_, j_]/; j>i:=0; T[i_, j_]:=T[i, j]=T[i-1, j]-T[i, j-1]+2 T[i-1, j-1]
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CROSSREFS
| Cf. A086990, A090412, A049122, A009766, A065432, A065441.
Sequence in context: A168532 A093555 A065432 * A078805 A122837 A143359
Adjacent sequences: A094181 A094182 A094183 * A094185 A094186 A094187
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KEYWORD
| sign,tabl
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AUTHOR
| Wouter Meeussen (wouter.meeussen(AT)pandora.be), May 06 2004
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