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 A095944 Number of subsets S of {1,2,...,n} which contain a number that is greater than the sum of the other numbers in S. 6
 1, 3, 6, 11, 18, 28, 42, 61, 86, 119, 162, 217, 287, 375, 485, 622, 791, 998, 1251, 1558, 1929, 2376, 2912, 3552, 4314, 5218, 6287, 7548, 9031, 10770, 12805, 15180, 17945, 21158, 24883, 29193, 34171, 39909, 46511, 54095, 62792, 72749, 84132, 97125 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Convolution of A000009 and A001477. - Vaclav Kotesovec, Mar 12 2016 LINKS T. D. Noe and Alois P. Heinz, Table of n, a(n) for n = 1..10000 (first 500 terms from T. D. Noe) FORMULA Second differences are A000009, partitions into distinct parts. Proof from Fred W. Helenius (fredh(AT)ix.netcom.com): Let k be the largest element (the "dictator") in S and let j be the sum of the remaining elements, so 0 <= j < k. For a given k and j, the number of subsets S is just the number of partitions j into distinct parts; call that a(j). Then b(n) = Sum_{1<=k<=n} Sum_{0<=j=1} (1 + x^k). - Ilya Gutkovskiy, Jan 03 2017 EXAMPLE a(3) = 6 since the subsets {1},{2},{3},{1,2},{1,3},{2,3} are the only subsets of {1,2,3} which contain a number greater than the sum of the other numbers in the set. MATHEMATICA r[s_, x_] := r[s, x] = 1 + Sum[r[s-i, i-1], {i, Min[x, s]}]; f[n_] := Sum[r[k-1, k-1], {k, n}]; Array[f, 50] (* Giovanni Resta, Mar 16 2006 *) Accumulate[ Accumulate[q = PartitionsQ[ Range[1, 50]]]+1] - Accumulate[q] (* Jean-François Alcover, Nov 14 2011 *) CROSSREFS Equals 2^n - 1 - A095941(n). Sequence in context: A011849 A173690 A178855 * A014284 A118482 A281689 Adjacent sequences:  A095941 A095942 A095943 * A095945 A095946 A095947 KEYWORD nice,nonn,easy AUTHOR W. Edwin Clark, Jul 13 2004 EXTENSIONS More terms from John W. Layman, Aug 10 2004 More terms from Giovanni Resta, Mar 16 2006 STATUS approved

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Last modified May 23 11:20 EDT 2019. Contains 323514 sequences. (Running on oeis4.)