A169953 Third entry in row n of triangle in A169950.

1, 1, 4, 8, 15, 23, 44, 64, 117, 173, 262, 374, 571, 791, 1188, 1644, 2355, 3205, 4552, 5980, 8283, 10925, 14702, 19338, 26031, 33581, 44690, 57566, 75531, 96531, 125738, 158690, 204953, 258325, 329394, 412054, 523931, 649973, 822434, 1018332, 1274909

Offset: 2

Author

N. J. A. Sloane, Aug 01 2010

Keywords

• nonn

Comments

Wanted: a recurrence. Are any of A169940-A169954 related to any other entries in the OEIS?

Links

• Index entries for sequences related to carryless arithmetic

Crossrefs

Related to thickness: A169940-A169954, A061909.

Programs

Mathematica

b[n_, s_] := b[n, s] = Module[{sn, m}, m = Length[s]; sn = Append[s, n]; If[n < 1, 1, b[n - 1, s] + If[m*(m + 1)/2 == Length[Union[Flatten[Table[ sn[[i]] + sn[[j]], {i, 1, m}, {j, i + 1, m + 1}]]]], b[n - 1, sn], 0]]];
A196723[n_] := A196723[n] = b[n - 1, {n}] + If[n == 0, 0, A196723[n - 1]]; c[n_, s_] := c[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], c[n-1, sn], 0] + c[n-1, s]]];
A143823[n_] := A143823[n] = c[n - 1, {n}] + If[n == 0, 0, A143823[n - 1]];
a[n_] := A196723[n+1] - A196723[n] - A143823[n+1] + A143823[n];
Table[Print[n, " ", a[n]]; a[n], {n, 2, 42}] (* Jean-François Alcover, Sep 07 2019, after Alois P. Heinz in A196723 and A143823 *)

Formula

a(n) = A169948(n)-A169948(n-1) for n>2. - Andrew Howroyd, Jul 09 2017

Extensions

a(15)-a(28) and definition corrected by Nathaniel Johnston, Nov 15 2010

Offset corrected and a(30)-a(42) from Andrew Howroyd, Jul 09 2017