

A191671


Dispersion of A004772 (>1 and congruent to 0 or 2 or 3 mod 4), by antidiagonals.


7



1, 2, 5, 3, 7, 9, 4, 10, 12, 13, 6, 14, 16, 18, 17, 8, 19, 22, 24, 23, 21, 11, 26, 30, 32, 31, 28, 25, 15, 35, 40, 43, 42, 38, 34, 29, 20, 47, 54, 58, 56, 51, 46, 39, 33, 27, 63, 72, 78, 75, 68, 62, 52, 44, 37, 36, 84, 96, 104, 100, 91, 83, 70, 59, 50, 41
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OFFSET

1,2


COMMENTS

For a background discussion of dispersions, see A191426.
...
Each of the sequences (4n, n>2), (4n+1, n>0), (3n+2, n>=0), generates a dispersion. Each complement (beginning with its first term >1) also generates a dispersion. The six sequences and dispersions are listed here:
...
...
EXCEPT for at most 2 initial terms (so that column 1 always starts with 1):
...
Regarding the dispersions A191670A191673, there is a formula for sequences of the type "(a or b or c mod m)", (as in the Mathematica program below):
If f(n)=(n mod 3), then (a,b,c,a,b,c,a,b,c,...) is given by
a*f(n+2)+b*f(n+1)+c*f(n), so that "(a or b or c mod m)" is given by
a*f(n+2)+b*f(n+1)+c*f(n)+m*floor((n1)/3)), for n>=1.


LINKS



EXAMPLE

Northwest corner:
1....2....3....4....6
5....7....10...14...19
9....12...16...22...30
13...18...24...32...43
17...23...31...42...56


MATHEMATICA

(* Program generates the dispersion array T of the increasing sequence f[n] *)
r = 40; r1 = 12; c = 40; c1 = 12;
a = 2; b = 3; c2 = 4; m[n_] := If[Mod[n, 3] == 0, 1, 0];
f[n_] := a*m[n + 2] + b*m[n + 1] + c2*m[n] + 4*Floor[(n  1)/3]
Table[f[n], {n, 1, 30}] (* A004772 *)
mex[list_] := NestWhile[#1 + 1 &, 1, Union[list][[#1]] <= #1 &, 1, Length[Union[list]]]
rows = {NestList[f, 1, c]};
Do[rows = Append[rows, NestList[f, mex[Flatten[rows]], r]], {r}];
t[i_, j_] := rows[[i, j]];
TableForm[Table[t[i, j], {i, 1, 10}, {j, 1, 10}]] (* A191671 *)
Flatten[Table[t[k, n  k + 1], {n, 1, c1}, {k, 1, n}]] (* A191671 *)


CROSSREFS



KEYWORD



AUTHOR



STATUS

approved



