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 A159916 Triangle T(m,n) = number of subsets of {1,...,m} with n elements having an odd sum, 1 <= n <= m. 10
 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, 0 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS 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 (p-> seq(coeff(p, x, i), i=1..n))(b(n, 0)): seq(T(n), n=1..15);  # Alois P. Heinz, Feb 04 2017 MATHEMATICA b[n_, s_] := b[n, s] = Expand[If[n==0, s, b[n-1, s] + x*b[n-1, Mod[s+n, 2]] ]]; T[n_] := Function[p, Table[Coefficient[p, x, i], {i, 1, n}]][b[n, 0]]; Table[T[n], {n, 1, 15}] // Flatten (* Jean-François Alcover, Nov 17 2017, after Alois P. Heinz *) PROG (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 ) CROSSREFS Cf. A004526, A007318, A133872, A282011. T(2n,n) gives A110145. Sequence in context: A171933 A074823 A226177 * A159286 A261277 A006462 Adjacent sequences:  A159913 A159914 A159915 * A159917 A159918 A159919 KEYWORD nonn,tabl AUTHOR M. F. Hasler, Apr 30 2009 STATUS approved

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Last modified March 30 12:10 EDT 2020. Contains 333125 sequences. (Running on oeis4.)