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Search: id:A080233
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| A080233 |
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Triangle T(n,k) obtained by taking differences of consecutive pairs of row elements of Pascal's triangle A007318. |
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+0
3
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| 1, 1, 0, 1, 1, -1, 1, 2, 0, -2, 1, 3, 2, -2, -3, 1, 4, 5, 0, -5, -4, 1, 5, 9, 5, -5, -9, -5, 1, 6, 14, 14, 0, -14, -14, -6, 1, 7, 20, 28, 14, -14, -28, -20, -7, 1, 8, 27, 48, 42, 0, -42, -48, -27, -8
(list; graph; listen)
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OFFSET
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0,8
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COMMENT
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Row sums are 1,1,1,1,1,1 with G.f. 1/(1-x) Can also be obtained from triangle A080232 by taking sums of pairs of consecutive row elements
Mirror image of triangle in A156644. [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Feb 14 2009]
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FORMULA
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T(n, k) = if(k>n, 0, binomial(n, k)-binomial(n, k-1))
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EXAMPLE
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Rows are {1}, {1,0}, {1,1,-1}, {1,2,0,-2}, {1,3,2,-2,-3}, ...
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CROSSREFS
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Cf. A007318, A080232.
Sequence in context: A029221 A029183 A138110 this_sequence A156644 A097808 A114325
Adjacent sequences: A080230 A080231 A080232 this_sequence A080234 A080235 A080236
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KEYWORD
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easy,sign
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AUTHOR
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Paul Barry (pbarry(AT)wit.ie), Feb 10 2003
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