This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A191668 #23 Oct 18 2017 05:06:34
%S A191668 1,2,3,6,10,4,22,38,14,5,86,150,54,18,7,342,598,214,70,26,8,1366,2390,
%T A191668 854,278,102,30,9,5462,9558,3414,1110,406,118,34,11,21846,38230,13654,
%U A191668 4438,1622,470,134,42,12,87382,152918,54614,17750,6486,1878,534,166
%N A191668 Dispersion of A016825 (4k+2, k>0), by antidiagonals.
%C A191668 For a background discussion of dispersions, see A191426.
%C A191668 ...
%C A191668 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:
%C A191668 ...
%C A191668 A191452=dispersion of A008586 (4k, k>=1)
%C A191668 A191667=dispersion of A016813 (4k+1, k>=1)
%C A191668 A191668=dispersion of A016825 (4k+2, k>=0)
%C A191668 A191669=dispersion of A004767 (4k+3, k>=0)
%C A191668 A191670=dispersion of A042968 (1 or 2 or 3 mod 4 and >=2)
%C A191668 A191671=dispersion of A004772 (0 or 1 or 3 mod 4 and >=2)
%C A191668 A191672=dispersion of A004773 (0 or 1 or 2 mod 4 and >=2)
%C A191668 A191673=dispersion of A004773 (0 or 2 or 3 mod 4 and >=2)
%C A191668 ...
%C A191668 EXCEPT for at most 2 initial terms (so that column 1 always starts with 1):
%C A191668 A191452 has 1st col A042968, all else A008486
%C A191668 A191667 has 1st col A004772, all else A016813
%C A191668 A191668 has 1st col A042965, all else A016825
%C A191668 A191669 has 1st col A004773, all else A004767
%C A191668 A191670 has 1st col A008486, all else A042968
%C A191668 A191671 has 1st col A016813, all else A004772
%C A191668 A191672 has 1st col A016825, all else A042965
%C A191668 A191673 has 1st col A004767, all else A004773
%C A191668 ...
%C A191668 Regarding the dispersions A191670-A191673, there is a formula for sequences of the type "(a or b or c mod m)", (as in the Mathematica program below):
%C A191668 If f(n)=(n mod 3), then (a,b,c,a,b,c,a,b,c,...) is given by
%C A191668 a*f(n+2)+b*f(n+1)+c*f(n), so that "(a or b or c mod m)" is given by
%C A191668 a*f(n+2)+b*f(n+1)+c*f(n)+m*floor((n-1)/3)), for n>=1.
%H A191668 Ivan Neretin, <a href="/A191668/b191668.txt">Table of n, a(n) for n = 1..5050</a> (first 100 antidiagonals, flattened)
%F A191668 Conjecture: a(n,k) = (8 + (3*floor((4*n + 1)/3) - 2)*4^k)/12 = (8 + (3*A042965(n+1) - 2)*A000302(k))/12. - _L. Edson Jeffery_, Feb 14 2015
%e A191668 Northwest corner:
%e A191668 . 1 2 6 22 86 342 1366 5462 21846 87382
%e A191668 . 3 10 38 150 598 2390 9558 38230 152918 611670
%e A191668 . 4 14 54 214 854 3414 13654 54614 218454 873814
%e A191668 . 5 18 70 278 1110 4438 17750 70998 283990 1135958
%e A191668 . 7 26 102 406 1622 6486 25942 103766 415062 1660246
%e A191668 . 8 30 118 470 1878 7510 30038 120150 480598 1922390
%e A191668 . 9 34 134 534 2134 8534 34134 136534 546134 2184534
%e A191668 . 11 42 166 662 2646 10582 42326 169302 677206 2708822
%e A191668 . 12 46 182 726 2902 11606 46422 185686 742742 2970966
%e A191668 . 13 50 198 790 3158 12630 50518 202070 808278 3233110
%t A191668 (* Program generates the dispersion array T of the increasing sequence f[n] *)
%t A191668 r = 40; r1 = 12; c = 40; c1 = 12;
%t A191668 f[n_] := 4*n-2
%t A191668 Table[f[n], {n, 1, 30}] (* A016825 *)
%t A191668 mex[list_] := NestWhile[#1 + 1 &, 1, Union[list][[#1]] <= #1 &, 1, Length[Union[list]]]
%t A191668 rows = {NestList[f, 1, c]};
%t A191668 Do[rows = Append[rows, NestList[f, mex[Flatten[rows]], r]], {r}];
%t A191668 t[i_, j_] := rows[[i, j]];
%t A191668 TableForm[Table[t[i, j], {i, 1, 10}, {j, 1, 10}]] (* A191668 *)
%t A191668 Flatten[Table[t[k, n - k + 1], {n, 1, c1}, {k, 1, n}]] (* A191668 *)
%t A191668 (* Conjectured: *) Grid[Table[(8 + (3*Floor[(4*n + 1)/3] - 2)*4^k)/12, {n, 10}, {k, 10}]] (* _L. Edson Jeffery_, Feb 14 2015 *)
%Y A191668 Row 1: A047849.
%Y A191668 Cf. A000302, A042965, A016825, A191672, A191426.
%K A191668 nonn,tabl
%O A191668 1,2
%A A191668 _Clark Kimberling_, Jun 11 2011