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Search: id:A080418
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| A080418 |
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Generalized Pascal triangle. |
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+0
1
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| 1, 1, 3, 1, 2, 4, 1, 5, 5, 5, 1, 4, 11, 9, 6, 1, 7, 14, 21, 14, 7, 1, 6, 22, 34, 36, 20, 8, 1, 9, 27, 57, 69, 57, 27, 9, 1, 8, 37, 83, 127, 125, 85, 35, 10, 1, 11, 44, 121, 209, 253, 209, 253, 209, 121, 44, 11, 1, 10, 56, 164, 331, 461, 463, 329, 166, 54, 12
(list; table; graph; listen)
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OFFSET
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1,3
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FORMULA
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T(n, 1)=1, T(1, k)=0, k>1, T(n, 2)=T(n-1, 1)+T(n-1, 2)+(-2)^(n+k), T(n, k)=T(n-1, k-1)+T(n-1, k)+(-1)^(n+k), k>2
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EXAMPLE
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Rows are {1}, {1,3}, {1,2,4}, {1,5,5,5}, {1,4,11,9,6},{1,7,14,21,14,7},... For example, 2=1+3-2,5=1+2+2; 11=5+5+1,14=4+11-1
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CROSSREFS
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Columns include A000012, A004442, A000217+(-1)^n, A000292+(-1)^n and in general, binomial(n+k, k)+(-1)^n. Diagonals include A000096, A063258.
Sequence in context: A130419 A083110 A059016 this_sequence A073892 A004608 A117905
Adjacent sequences: A080415 A080416 A080417 this_sequence A080419 A080420 A080421
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KEYWORD
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easy,nonn,tabl
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AUTHOR
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Paul Barry (pbarry(AT)wit.ie), Feb 18 2003
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