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 A294479 Solution of the complementary equation a(n) = a(n-2) + b(n-1) + n, where a(0) = 1, a(1) = 3, b(0) = 2. 2
 1, 3, 7, 11, 17, 24, 32, 41, 52, 63, 76, 89, 104, 120, 137, 155, 174, 194, 215, 238, 261, 286, 311, 338, 365, 394, 424, 455, 487, 520, 554, 589, 625, 662, 701, 740, 781, 822, 865, 908, 953, 998, 1045, 1092, 1142, 1191, 1243, 1294, 1348, 1401, 1457, 1512 (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 A294476 for a guide to related sequences. LINKS Clark Kimberling, Table of n, a(n) for n = 0..1000 Clark Kimberling, Complementary equations, J. Int. Seq. 19 (2007), 1-13. EXAMPLE a(0) = 1, a(1) = 3, b(0) = 2, b(1) = 4, so that a(2)  = a(0) + b(1) + 2 = 7 Complement: (b(n)) = (2, 4, 5, 6, 8, 9, 10, 12, 13, 14, ...) MATHEMATICA mex := First[Complement[Range[1, Max[#1] + 1], #1]] &; a[0] = 1; a[1] = 3; b[0] = 2; a[n_] := a[n] = a[n - 2] + b[n - 1] + n; b[n_] := b[n] = mex[Flatten[Table[Join[{a[n]}, {a[i], b[i]}], {i, 0, n - 1}]]]; Table[a[n], {n, 0, 40}]  (* A294479 *) Table[b[n], {n, 0, 10}] CROSSREFS Cf. A293076, A293765, A294476. Sequence in context: A262502 A211076 A180452 * A331968 A029715 A088803 Adjacent sequences:  A294476 A294477 A294478 * A294480 A294481 A294482 KEYWORD nonn,easy AUTHOR Clark Kimberling, Nov 01 2017 STATUS approved

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Last modified September 27 18:56 EDT 2021. Contains 347694 sequences. (Running on oeis4.)