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 A238687 Number of partitions p of n such that no three points (i,p_i), (j,p_j), (k,p_k) are collinear, where p_i denotes the i-th part. 6
 1, 1, 2, 2, 4, 5, 6, 8, 13, 10, 18, 21, 27, 29, 41, 41, 62, 65, 77, 91, 114, 127, 151, 173, 213, 232, 279, 322, 372, 410, 491, 518, 630, 724, 814, 894, 1057, 1141, 1326, 1502, 1681, 1839, 2146, 2324, 2636, 2966, 3272, 3607, 4173, 4422, 5035, 5616, 6195, 6703 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Fausto A. C. Cariboni, Table of n, a(n) for n = 0..300 (terms 0..150 from Alois P. Heinz) EXAMPLE There are a(10) = 18 such partitions of 10: [6,2,1,1], [5,2,2,1], [4,4,1,1], [3,3,2,2], [8,1,1], [7,2,1], [6,3,1], [6,2,2], [5,4,1], [5,3,2], [4,4,2], [4,3,3], [9,1], [8,2], [7,3], [6,4], [5,5], [10]. MAPLE b:= proc(n, i, l) local j, k, m; m:= nops(l);       for j to m-2 do for k from j+1 to m-1 do         if (l[m]-l[k])*(k-j)=(l[k]-l[j])*(m-k)           then return 0 fi od od;      `if`(n=0, 1, `if`(i<1, 0, b(n, i-1, l)+      `if`(i>n, 0, b(n-i, i, [l[], i]))))     end: a:= n-> b(n, n, []): seq(a(n), n=0..40); MATHEMATICA b[n_, i_, l_] := Module[{j, k, m = Length[l]}, For[j = 1, j <= m - 2, j++, For[k = j+1, k <= m-1, k++, If[(l[[m]] - l[[k]])*(k - j) == (l[[k]] - l[[j]])*(m - k), Return[0]]]]; If[n == 0, 1, If[i < 1, 0, b[n, i - 1, l] + If[i > n, 0, b[n - i, i, Append[l, i]]]]]]; a[n_] := b[n, n, {}]; Table[a[n], {n, 0, 40}] (* Jean-François Alcover, May 21 2018, translated from Maple *) CROSSREFS Cf. A238686 (the same for compositions). Cf. A238424, A238433, A238571. Sequence in context: A238571 A325874 A293957 * A238433 A238424 A121269 Adjacent sequences:  A238684 A238685 A238686 * A238688 A238689 A238690 KEYWORD nonn AUTHOR Joerg Arndt and Alois P. Heinz, Mar 02 2014 STATUS approved

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Last modified April 17 18:52 EDT 2021. Contains 343070 sequences. (Running on oeis4.)