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A080232
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Triangle T(n,k) of differences of pairs of consecutive terms of triangle A071919.
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4
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1, 1, -1, 1, 0, -1, 1, 1, -1, -1, 1, 2, 0, -2, -1, 1, 3, 2, -2, -3, -1, 1, 4, 5, 0, -5, -4, -1, 1, 5, 9, 5, -5, -9, -5, -1, 1, 6, 14, 14, 0, -14, -14, -6, -1, 1, 7, 20, 28, 14, -14, -28, -20, -7, -1, 1, 8, 27, 48, 42, 0, -42, -48, -27, -8, -1
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,12
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COMMENTS
| Row sums are 1,0,0,0,0,0, ... with G.f. 1 = (1-x)^0(1-2x)^0
(1,-1)-Pascal triangle ; mirror image of triangle A112467 . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 07 2006
Triangle T(n,k), read by rows, given by (1,0,0,0,0,0,0,0,0,...) DELTA (-1,2,0,0,0,0,0,0,0,...) where DELTA is the operator defined in A084938. - From DELEHAM Philippe, Nov 01 2011
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FORMULA
| T(n, k)= binomial(n, k)+2Sum{j=1...k, (-1)^j binomial(n, k-j))
Sum_{k, 0<=k<=n} T(n, k)*x^k = (1-x)*(1+x)^(n-1), for n>=1 . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Sep 05 2005
T(n,k)=T(n-1,k-1)+T(n-1,k) with T(n,0)=1, T(n,n)=-1 for n>0.- From DELEHAM Philippe, Nov 01 2011
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EXAMPLE
| Rows {1}, {1,-1}, {1,0,-1}, {1,1,-1,-1}, {1,2,0,-2,-1}, ...
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CROSSREFS
| Cf. A071919, A007318.
Apart from initial term, same as A037012.
Sequence in context: A175929 A079627 A061398 * A008482 A037012 A112467
Adjacent sequences: A080229 A080230 A080231 * A080233 A080234 A080235
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KEYWORD
| easy,sign,tabl
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Feb 09 2003
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