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A169948 Fourth entry in row n of triangle in A169945. 1
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 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois 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: A249665 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

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Last modified June 3 05:29 EDT 2020. Contains 334798 sequences. (Running on oeis4.)