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Search: id:A122070
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| A122070 |
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Triangle T(n,k), 0<=k<=n, given by T(n,k)=Fibonacci(n+k+1)*binomial(n,k). |
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1
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| 1, 1, 2, 2, 6, 5, 3, 15, 24, 13, 5, 32, 78, 84, 34, 8, 65, 210, 340, 275, 89, 13, 126, 510, 1100, 1335, 864, 233
(list; table; graph; listen)
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OFFSET
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0,3
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FORMULA
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T(n,k)=A000045(n+k+1)*A007318(n,k) . T(n,n)=Fibonacci(2*n+1)=A001519(n+1) . Sum_{k, 0<=k<=n}T(n,k)=Fibonacci(3*n+1)=A033887(n) . Sum_{k, 0<=k<=n}(-1)^k*T(n,k)=(-1)^n=A033999(n) . Sum_{k, 0<=k<=[n/2]}T(n-k,k)=(Fibonacci(n+1))^2=A007598(n+1).
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EXAMPLE
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Triangle begins:
1;
1, 2;
2, 6, 5;
3, 15, 24, 13;
5, 32, 78, 84, 34;
8, 65, 210, 340, 275, 89;
13, 126, 510, 1100, 1335, 864, 233;
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CROSSREFS
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Sequence in context: A064766 A121178 A019749 this_sequence A115255 A055924 A054917
Adjacent sequences: A122067 A122068 A122069 this_sequence A122071 A122072 A122073
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KEYWORD
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nonn,tabl
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AUTHOR
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Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Oct 15 2006
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