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A159916
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Triangle T[m,n] = number of subsets of {1,...,m} with n elements having an odd sum, 1 <= n <= m.
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6
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1, 1, 1, 2, 2, 0, 2, 4, 2, 0, 3, 6, 4, 2, 1, 3, 9, 10, 6, 3, 1, 4, 12, 16, 16, 12, 4, 0, 4, 16, 28, 32, 28, 16, 4, 0, 5, 20, 40, 60, 66, 44, 16, 4, 1, 5, 25, 60, 100, 126, 110, 60, 20, 5, 1, 6, 30, 80, 160, 236, 236, 160, 80, 30, 6, 0, 6, 36, 110, 240, 396, 472, 396, 240, 110, 36, 6
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OFFSET
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1,4
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COMMENTS
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One could extend the triangle to include values for m=0 and/or n=0, but these correspond to empty sets and would always be 0. The first odd value for odd m and 1<n<m is T[13,5] = 651.
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LINKS
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Table of n, a(n) for n=1..77.
Project Euler, Problem 242: Odd Triplets, April 25, 2009.
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FORMULA
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T[m,m] = A133872(m-1), T[m,1] = A004526(m+1).
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EXAMPLE
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The triangle starts:
(m=1) 1,
(m=2) 1,1,
(m=3) 2,2,0,
(m=4) 2,4,2,0,
(m=5) 3,6,4,2,1,
...
T(5,3)=4, since the set {1,2,3,4,5} has four 3-element subsets having an odd sum of elements, namely {1,2,4}, {1,3,5}, {2,3,4} and {2,4,5}.
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PROG
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(PARI) T(n, k)=sum( i=2^k-1, 2^n-2^(n-k), norml2(binary(i))==k & sum(j=0, n\2, bittest(i, 2*j))%2 )
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CROSSREFS
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Sequence in context: A105673 A171933 A074823 * A159286 A006462 A008281
Adjacent sequences: A159913 A159914 A159915 * A159917 A159918 A159919
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KEYWORD
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nonn,tabl
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AUTHOR
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M. F. Hasler, Apr 30 2009
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STATUS
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approved
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