A169948 Fourth entry in row n of triangle in A169945.

1, 2, 6, 14, 29, 52, 96, 160, 277, 450, 712, 1086, 1657, 2448, 3636, 5280, 7635, 10840, 15392, 21372, 29655, 40580, 55282, 74620, 100651, 134232, 178922, 236488, 312019, 408550, 534288, 692978, 897931, 1156256, 1485650, 1897704, 2421635, 3071608, 3894042

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.

Cf. A143823, A196723.

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_] := a[n] = A196723[n + 1] - A143823[n + 1];
Table[Print[n, " ", a[n]]; a[n], {n, 2, 40}] (* Jean-François Alcover, Aug 27 2019, after Alois P. Heinz in A196723 and A143823 *)

Formula

a(n) = A196723(n+1) - A143823(n+1). - Andrew Howroyd, Jul 09 2017

Extensions

a(15)-a(28) from Nathaniel Johnston, Nov 12 2010

a(29)-a(40) from Andrew Howroyd, Jul 09 2017