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A294865 Solution of the complementary equation a(n) = a(n-2) + 2*b(n-2), where a(0) = 1, a(1) = 2, b(0) = 3, and (a(n)) and (b(n)) are increasing complementary sequences. 2
1, 2, 7, 10, 17, 22, 33, 40, 55, 64, 81, 92, 111, 124, 147, 162, 187, 204, 233, 252, 283, 304, 337, 360, 395, 420, 457, 484, 525, 554, 597, 628, 673, 706, 755, 790, 841, 878, 931, 970, 1025, 1066, 1123, 1166, 1225, 1270, 1331, 1378, 1443, 1492, 1559, 1610 (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) + 2*b(0) = 7
Complement: (b(n)) = (3, 4, 5, 6, 8, 9, 11, 12, 13, 14, 15, ...)
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] + 2*b[n - 2];
b[n_] := b[n] = mex[Flatten[Table[Join[{a[n]}, {a[i], b[i]}], {i, 0, n - 1}]]];
Table[a[n], {n, 0, 18}] (* A294865 *)
Table[b[n], {n, 0, 10}]
CROSSREFS
Cf. A294860.
Sequence in context: A059316 A295825 A140115 * A105770 A240469 A257335
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Nov 16 2017
STATUS
approved

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Last modified June 24 08:39 EDT 2024. Contains 373663 sequences. (Running on oeis4.)