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

2,3

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..42.

Index entries for sequences related to carryless arithmetic

Formula

a(n) = A169948(n)-A169948(n-1) for n>2. - 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_] := 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 *)

Crossrefs

Related to thickness: A169940-A169954, A061909.

Sequence in context: A126255 A267682 A194804 * A213035 A014146 A049845

Adjacent sequences: A169950 A169951 A169952 * A169954 A169955 A169956

Keyword

nonn

Author

N. J. A. Sloane, Aug 01 2010

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

Status

approved