A295755
Solution of the complementary equation a(n) = a(n-1) + a(n-3) + a(n-4) + b(n-3), where a(0) = 1, a(1) = 2, a(2) = 3, a(3) = 4, b(0) = 5, b(1) = 6, b(2) = 7, b(3) = 8, and (a(n)) and (b(n)) are increasing complementary sequences.
Original entry on oeis.org
1, 2, 3, 4, 13, 25, 40, 66, 114, 190, 308, 502, 821, 1335, 2162, 3503, 5678, 9195, 14881, 24084, 38980, 63080, 102071, 165162, 267250, 432430, 699693, 1132136, 1831848, 2964004, 4795867, 7759886, 12555774, 20315682, 32871473, 53187172, 86058669, 139245866
Offset: 0
a(0) = 1, a(1) = 2, a(2) = 3, a(3) = 4, b(0) = 5, b(1) = 6, b(2) = 7, b(3) = 8, so that
b(4) = 9 (least "new number")
a(4) = a(3) + a(1) + a(0) + b(1) = 13
Complement: (b(n)) = (5, 6, 7, 8, 9, 10, 11, 12, 14, 15, ...)
-
mex := First[Complement[Range[1, Max[#1] + 1], #1]] &;
a[0] = 1; a[1] = 2; a[2] = 3; a[3] = 4;
b[0] = 5; b[1] = 6; b[2] = 7; b[3] = 8;
a[n_] := a[n] = a[n - 1] + a[n - 3] + a[n - 4] + b[n - 3];
b[n_] := b[n] = mex[Flatten[Table[Join[{a[n]}, {a[i], b[i]}], {i, 0, n - 1}]]];
z = 36; Table[a[n], {n, 0, z}] (* A295755 *)
Table[b[n], {n, 0, 20}] (*complement *)
A295756
Solution of the complementary equation a(n) = a(n-1) + a(n-3) + a(n-4) + b(n-2), where a(0) = 1, a(1) = 2, a(2) = 3, a(3) = 4, b(0) = 5, b(1) = 6, b(2) = 7, b(3) = 8, and (a(n)) and (b(n)) are increasing complementary sequences.
Original entry on oeis.org
1, 2, 3, 4, 14, 27, 43, 71, 123, 205, 332, 541, 885, 1439, 2330, 3775, 6119, 9909, 16036, 25953, 42005, 67975, 109990, 177976, 287985, 465980, 753977, 1219970, 1973968, 3193959, 5167941, 8361915, 13529879, 21891817, 35421712, 57313546, 92735283, 150048854
Offset: 0
a(0) = 1, a(1) = 2, a(2) = 3, a(3) = 4, b(0) = 5, b(1) = 6, b(2) = 7, b(3) = 8, so that
b(4) = 9 (least "new number")
a(4) = a(3) + a(1) + a(0) + b(2) = 14
Complement: (b(n)) = (5, 6, 7, 8, 9, 10, 11, 12, 13, 15, ...)
-
mex := First[Complement[Range[1, Max[#1] + 1], #1]] &;
a[0] = 1; a[1] = 2; a[2] = 3; a[3] = 4;
b[0] = 5; b[1] = 6; b[2] = 7; b[3] = 8;
a[n_] := a[n] = a[n - 1] + a[n - 3] + a[n - 4] + b[n - 2];
b[n_] := b[n] = mex[Flatten[Table[Join[{a[n]}, {a[i], b[i]}], {i, 0, n - 1}]]];
z = 36; Table[a[n], {n, 0, z}] (* A295756 *)
Table[b[n], {n, 0, 20}] (*complement *)
A295757
Solution of the complementary equation a(n) = a(n-1) + a(n-3) + a(n-4) + b(n-1), where a(0) = 1, a(1) = 2, a(2) = 3, a(3) = 4, b(0) = 5, b(1) = 6, b(2) = 7, b(3) = 8, and (a(n)) and (b(n)) are increasing complementary sequences.
Original entry on oeis.org
1, 2, 3, 4, 15, 29, 46, 76, 132, 220, 356, 580, 949, 1543, 2498, 4047, 6560, 10623, 17191, 27822, 45030, 72870, 117910, 190790, 308720, 499531, 808263, 1307806, 2116091, 3423920, 5540025, 8963959, 14504008, 23467992, 37972016, 61440024, 99412066, 160852117
Offset: 0
a(0) = 1, a(1) = 2, a(2) = 3, a(3) = 4, b(0) = 5, b(1) = 6, b(2) = 7, b(3) = 8, so that
b(4) = 9 (least "new number")
a(4) = a(3) + a(1) + a(0) + b(3) = 15
Complement: (b(n)) = (5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 16, ...)
-
mex := First[Complement[Range[1, Max[#1] + 1], #1]] &;
a[0] = 1; a[1] = 2; a[2] = 3; a[3] = 4;
b[0] = 5; b[1] = 6; b[2] = 7; b[3] = 8;
a[n_] := a[n] = a[n - 1] + a[n - 3] + a[n - 4] + b[n - 1];
b[n_] := b[n] = mex[Flatten[Table[Join[{a[n]}, {a[i], b[i]}], {i, 0, n - 1}]]];
z = 36; Table[a[n], {n, 0, z}] (* A295757 *)
Table[b[n], {n, 0, 20}] (*complement *)
Showing 1-3 of 3 results.
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