OFFSET
0,9
COMMENTS
LINKS
Fausto A. C. Cariboni, Rows n = 0..80, flattened (rows n = 0..40 from Alois P. Heinz)
Eric Weisstein's World of Mathematics, Nonaveraging Sequence
Wikipedia, Arithmetic progression
Wikipedia, Salem-Spencer set
EXAMPLE
1;
0, 1;
0, 1, 1;
0, 1, 2;
0, 1, 3, 2;
0, 1, 4, 4, 1;
0, 1, 5, 8, 3;
0, 1, 6, 12, 6;
0, 1, 7, 18, 15;
0, 1, 8, 24, 26, 4;
0, 1, 9, 32, 47, 20;
0, 1, 10, 40, 67, 40, 7;
0, 1, 11, 50, 102, 80, 18;
0, 1, 12, 60, 140, 140, 53, 6;
0, 1, 13, 72, 194, 236, 110, 16, 1;
0, 1, 14, 84, 248, 342, 198, 42, 3;
0, 1, 15, 98, 326, 532, 377, 100, 10;
...
MAPLE
b:= proc(n, s) option remember; `if`(n=0, x, b(n-1, s)+ `if`(
ormap(j-> 2*j-n in s, s), 0, expand(x*b(n-1, s union {n}))))
end:
T:= n-> (p-> seq(coeff(p, x, i), i=0..degree(p)))(
`if`(n=0, 1, b(n-1, {n}))):
seq(T(n), n=0..16);
MATHEMATICA
b[n_, s_] := b[n, s] = If[n == 0, x, b[n-1, s] + If[
AnyTrue[s, MemberQ[s, 2#-n]&], 0, Expand[x*b[n-1, s ~Union~ {n}]]]];
T[n_] := If[n == 0, {1}, CoefficientList[b[n-1, {n}], x]];
T /@ Range[0, 16] // Flatten (* Jean-François Alcover, May 03 2021, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Alois P. Heinz, May 14 2020
STATUS
approved