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A294863 Solution of the complementary equation a(n) = a(n-2) + b(n-2) + 3, where a(0) = 1, a(1) = 2, b(0) = 3, and (a(n)) and (b(n)) are increasing complementary sequences. 3
1, 2, 7, 9, 15, 18, 26, 31, 40, 46, 56, 63, 75, 83, 97, 106, 121, 131, 147, 158, 175, 188, 206, 220, 239, 255, 275, 292, 313, 331, 353, 372, 395, 416, 440, 462, 487, 510, 537, 561, 589, 614, 643, 669, 699, 726, 757, 786, 818, 848, 881, 912, 946, 979, 1014 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
The increasing complementary sequences a() and b() are uniquely determined by the titular equation and initial values. See A294860 for a guide to related sequences.
LINKS
Clark Kimberling, Complementary equations, J. Int. Seq. 19 (2007), 1-13.
EXAMPLE
a(0) = 1, a(1) = 2, b(0) = 3
b(1) = 4 (least "new number")
a(2) = a(0) + b(0) + 3 = 7
Complement: (b(n)) = (3, 4, 5, 6, 8, 10, 11, 12, 13, 14, 16, ...)
MATHEMATICA
mex := First[Complement[Range[1, Max[#1] + 1], #1]] &;
a[0] = 1; a[1] = 2; b[0] = 3;
a[n_] := a[n] = a[n - 2] + b[n - 2] + 3;
b[n_] := b[n] = mex[Flatten[Table[Join[{a[n]}, {a[i], b[i]}], {i, 0, n - 1}]]];
Table[a[n], {n, 0, 18}] (* A294863 *)
Table[b[n], {n, 0, 10}]
CROSSREFS
Sequence in context: A226824 A168132 A211280 * A085544 A154789 A106352
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Nov 16 2017
STATUS
approved

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Last modified May 28 18:29 EDT 2024. Contains 372919 sequences. (Running on oeis4.)