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A122828
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Triangle T(n,k), 0<=k<=n, defined by : T(n,k)=0 if k<0, T(n,k)=0 if k>n,T(0,0)=1, T(1,0)=1, T(1,1)=2, T(n,k)=T(n-1,k-1)+T(n-1,k)+T(n-2,k).
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0
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1, 1, 2, 2, 3, 2, 3, 7, 5, 2, 5, 13, 14, 7, 2, 8, 25, 32, 23, 9, 2, 13, 46, 71, 62, 34, 11, 2, 34, 151, 304, 367, 295, 163, 62, 15, 2, 55, 269, 604, 827, 767, 505, 238, 79, 17, 2
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OFFSET
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0,3
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LINKS
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FORMULA
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Sum{k,0<=k<=n}T(n,k)=A078057(n) .T(n,0) = Fibonacci(n+1)=A000045(n+1).
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EXAMPLE
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Triangle begins:
1;
1, 2;
2, 3, 2;
3, 7, 5, 2;
5, 13, 14, 7, 2;
8, 25, 32, 23, 9, 2;
13, 46, 71, 62, 34, 11, 2;
21, 84, 149, 156, 105, 47, 13, 2;
34, 151, 304, 367, 295, 163, 62, 15, 2;
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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