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 A191666 Dispersion of A042964 (numbers congruent to 2 or 3 mod 4), by antidiagonals. 4
 1, 2, 4, 3, 7, 5, 6, 14, 10, 8, 11, 27, 19, 15, 9, 22, 54, 38, 30, 18, 12, 43, 107, 75, 59, 35, 23, 13, 86, 214, 150, 118, 70, 46, 26, 16, 171, 427, 299, 235, 139, 91, 51, 31, 17, 342, 854, 598, 470, 278, 182, 102, 62, 34, 20, 683, 1707, 1195, 939, 555, 363 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Row 1:  A005578 Row 2:  A160113 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: ... A191663=dispersion of A042948 (0 or 1 mod 4 and >1) A054582=dispersion of A005843 (0 or 2 mod 4 and >1; evens) A191664=dispersion of A014601 (0 or 3 mod 4 and >1) A191665=dispersion of A042963 (1 or 2 mod 4 and >1) A191448=dispersion of A005408 (1 or 3 mod 4 and >1, odds) A191666=dispersion of A042964 (2 or 3 mod 4) ... EXCEPT for at most 2 initial terms (so that column 1 always starts with 1): A191663 has 1st col A042964, all else A042948 A054582 has 1st col A005408, all else A005843 A191664 has 1st col A042963, all else A014601 A191665 has 1st col A014601, all else A042963 A191448 has 1st col A005843, all else A005408 A191666 has 1st col A042948, all else A042964 ... There is a formula for sequences of the type "(a or b mod m)", (as in the Mathematica program below):    If f(n)=(n mod 2), then (a,b,a,b,a,b,...) is given by    a*f(n+1)+b*f(n), so that "(a or b mod m)" is given by    a*f(n+1)+b*f(n)+m*floor((n-1)/2)), for n>=1. LINKS Ivan Neretin, Table of n, a(n) for n = 1..5050 (first 100 antidiagonals, flattened) EXAMPLE Northwest corner: 1...2...3....6...11 4...7...14....27...54 5...10...19...38...75 8...15..30...59...118 8...18..35...70...139 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; m[n_] := If[Mod[n, 2] == 0, 1, 0]; f[n_] := a*m[n + 1] + b*m[n] + 4*Floor[(n - 1)/2] Table[f[n], {n, 1, 30}]  (* A042964: (2+4k, 3+4k) *) 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}]] (* A191666 *) Flatten[Table[t[k, n - k + 1], {n, 1, c1}, {k, 1, n}]] (* A191666  *) CROSSREFS Cf. A042963, A014601, A191426, A191663. Sequence in context: A340245 A064357 A191735 * A215673 A120619 A346298 Adjacent sequences:  A191663 A191664 A191665 * A191667 A191668 A191669 KEYWORD nonn,tabl AUTHOR Clark Kimberling, Jun 11 2011 STATUS approved

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Last modified November 28 03:29 EST 2021. Contains 349400 sequences. (Running on oeis4.)