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Search: id:A065040
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| A065040 |
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Triangle T(m,k): maximal power of 2 dividing binomial coefficient binomial(m,k). |
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+0
3
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| 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 1, 2, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 2, 3, 1, 3, 2, 3, 0, 0, 0, 2, 2, 1, 1, 2, 2, 0, 0, 0, 1, 0, 3, 1, 2, 1, 3, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 2, 1, 2, 0, 3, 2, 3, 0, 2, 1, 2, 0, 0, 0, 1, 1, 0, 0, 2, 2, 0, 0, 1, 1, 0, 0
(list; table; graph; listen)
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OFFSET
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0,12
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FORMULA
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f(0, j) = 0 f(1, j ) = (A007814(j+1)) = (0 1 0 2 0 1 0 3 0 1 0 2 0 1 0 4... ) f(i, j) = (sum ( f(1, j+k) - f(1, k), 0 <= k <= j-1)
The n-th term a(n) is equal to the binomial coefficient binomial(m,k), where m=floor((1+sqr(8*n+1))/2)-1 and k=n-m(m+1)/2. Also a(n)=g(m)-g(k)-g(m-k), where g(x)=sum(floor(x/2^i), 1<=i<=floor(log_2(x))), m=floor((1+sqr(8*n+1))/2)-1, k=n-m(m+1)/2; - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), May 05 2007
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EXAMPLE
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0; 0,0; 0,1,0; 0,0,0,0; 0,2,1,2,0; ...
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CROSSREFS
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Cf. A007814 A001511 A000120 A049606 A000680 A048881 A011371 A005187 A000265 A001316.
Sequence in context: A079548 A079071 A050602 this_sequence A057595 A035201 A035179
Adjacent sequences: A065037 A065038 A065039 this_sequence A065041 A065042 A065043
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KEYWORD
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nonn,tabl
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AUTHOR
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Claude Lenormand (hlne.lenormand(AT)voono.net), Nov 05 2001
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