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

2,2

Comments

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

Links

Table of n, a(n) for n=2..40.

Index entries for sequences related to carryless arithmetic

Formula

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

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 *)

Crossrefs

Related to thickness: A169940-A169954, A061909.

Cf. A143823, A196723.

Sequence in context: A337106 A321027 A214907 * A192705 A123991 A112511

Adjacent sequences: A169945 A169946 A169947 * A169949 A169950 A169951

Keyword

nonn

Author

N. J. A. Sloane, Aug 01 2010

Extensions

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

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

Status

approved