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%I #29 Oct 08 2020 04:30:43
%S 1,3,8,16,29,49,82,130,205,305,450,654,947,1343,1902,2648,3675,5015,
%T 6824,9166,12343,16393,21762,28682,37695,49055,63892,82610,106691,
%U 136643,174862,222524,283073,357691,451538,567498,712817,890365,1112040,1382374,1717497
%N Third entry in row n of triangle in A169945.
%H Fausto A. C. Cariboni, <a href="/A169947/b169947.txt">Table of n, a(n) for n = 1..99</a> (terms 1..64 from Alois P. Heinz)
%H <a href="/index/Ca#CARRYLESS">Index entries for sequences related to carryless arithmetic</a>
%F Wanted: a recurrence. Are any of A169940-A169954 related to any other entries in the OEIS?
%F a(n) = A143823(n+1) - n - 2. - _Nathaniel Johnston_, Nov 12 2010
%t b[n_, s_] := Module[{sn, m}, If[n<1, 1, sn = Append[s, n]; m = Length[sn]; If[m*(m - 1)/2 == Length[Table[sn[[i]] - sn[[j]], {i, 1, m - 1}, {j, i+1, m}] // Flatten // Union], b[n - 1, sn], 0] + b[n - 1, s]]];
%t c[n_] := c[n] = b[n - 1, {n}] + If[n == 0, 0, c[n - 1]];
%t a[n_] := c[n + 1] - n - 2;
%t Table[Print[n, " ", a[n]]; a[n], {n, 1, 64}] (* _Jean-François Alcover_, Sep 02 2019, after _Alois P. Heinz_ in A143823 *)
%Y Related to thickness: A169940-A169954, A061909.
%K nonn
%O 1,2
%A _N. J. A. Sloane_, Aug 01 2010
%E More terms from _R. J. Mathar_, Aug 02 2010
%E a(22)-a(28) from _Nathaniel Johnston_, Nov 12 2010
%E More terms from _Alois P. Heinz_, Sep 16 2011
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