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%I #17 Dec 29 2024 09:06:20
%S 1,1,1,2,1,4,2,6,5,2,22,10,64,64,102,126,33,220,1902,132,2202,604,
%T 2120,942,22768,4044,234638,7436,614482,8264,107008,23776,11154697,
%U 4336,1152138,129812,37815814,245272,23068832,341506,12223534,427260,53970758,170064,133421946,4163944
%N Least positive unitary linear combination of distinct numbers in row n of Pascal's triangle; i.e., least positive sum of form d(0)C(n-1,0) + d(1)C(n-1,1) + ...+ d(m)C(n-1,m), d(i)=+-1, m = floor((n+1)/2).
%o (PARI) padbin(n, len) = my(b = binary(n)); while(length(b) < len, b = concat(0, b);); b;
%o a(n) = m = (n+1)\2; nb = 2^(m+1); lps = 0; v = vector(m, i, binomial(n-1, i-1)); for (i = 1, nb-1, vb = padbin(i, m+1); s = sum(k = 1, m, if (vb[k], v[k], -v[k])); if ((s>0), if (lps == 0, lps = s, if (s < lps, lps = s;);));); lps; \\ _Michel Marcus_, Sep 30 2013
%Y Cf. A007318 (Pascal's triangle).
%K nonn,changed
%O 1,4
%A _Clark Kimberling_
%E a(22)-a(43) from _Michel Marcus_, Sep 30 2013
%E a(44)-a(46) from _Michel Marcus_, Dec 29 2024