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Search: id:A108086
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| A108086 |
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Triangle, read by rows, where T(0,0) = 1, T(n,k) = (-1)^(n+k)*T(n-1,k) + T(n-1,k-1); a signed version of Pascal's triangle. |
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+0
1
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| 1, -1, 1, -1, -2, 1, 1, -3, -3, 1, 1, 4, -6, -4, 1, -1, 5, 10, -10, -5, 1, -1, -6, 15, 20, -15, -6, 1, 1, -7, -21, 35, 35, -21, -7, 1, 1, 8, -28, -56, 70, 56, -28, -8, 1, -1, 9, 36, -84, -126, 126, 84, -36, -9, 1, -1, -10, 45, 120, -210, -252, 210, 120, -45, -10, 1, 1, -11, -55, 165, 330, -462, -462, 330, 165, -55, -11, 1
(list; table; graph; listen)
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OFFSET
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0,5
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COMMENT
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Row sums are 1,0,-2,-4,-4,0,8,16,16,0,-32,-64,-64,0,128,256,256,... Antidiagonal sums are 1,-1,0,-1,-1,0,-1,1,0,1,1,0,1,-1,0,-1,-1,0,-1,1,0,1...
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FORMULA
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a(n, k) = (-1)^(int((n-k+1)/2)*A007318(n, k) (A007318 is Pascal's triangle).
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CROSSREFS
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Cf. A007318, A009116, A090132.
Sequence in context: A117440 A118433 A007318 this_sequence A130595 A108363 A076831
Adjacent sequences: A108083 A108084 A108085 this_sequence A108087 A108088 A108089
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KEYWORD
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sign,tabl
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AUTHOR
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Gerald McGarvey (gerald.mcgarvey(AT)comcast.net), Jun 05 2005
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