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 A003156 A self-generating sequence (see Comments for definition). (Formerly M3239) 10
 1, 4, 5, 6, 9, 12, 15, 16, 17, 20, 21, 22, 25, 26, 27, 30, 33, 36, 37, 38, 41, 44, 47, 48, 49, 52, 55, 58, 59, 60, 63, 64, 65, 68, 69, 70, 73, 76, 79, 80, 81, 84, 85, 86, 89, 90, 91, 94, 97, 100, 101, 102, 105, 106, 107, 110, 111, 112, 115, 118, 121, 122, 123, 126, 129, 132 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS From N. J. A. Sloane, Dec 26 2020: (Start) The best definitions of the triple [this sequence, A003157, A003158] are as the rows a(n), b(n), c(n) of the table: n: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, ... a: 1, 4, 5, 6, 9, 12, 15, 16, 17, 20, 21, 22, ... b: 3, 8, 11, 14, 19, 24, 29, 32, 35, 40, 43, 46, ... c: 2, 7, 10, 13, 18, 23, 28, 31, 34, 39, 42, 45, ... where a(1)=1, b(1)=3, c(1)=2, and thereafter a(n) = mex{a(i), b(i), c(i), i abc, b -> a, c -> a, starting with a(1) = a; see A092606 where a = 0, b = 2, c = 1. - Philippe Deléham, Apr 12 2004 REFERENCES N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS Alois P. Heinz, Table of n, a(n) for n = 1..1000 L. Carlitz, R. Scoville and V. E. Hoggatt, Jr., Fibonacci representations of higher order, Fib. Quart., 10 (1972), 43-69. [Here a, b, c are A003144, A003145, A003146.] L. Carlitz, R. Scoville, and V. E. Hoggatt, Jr., Representations for a special sequence, Fibonacci Quarterly 10.5 (1972), 499-518, 550. [A003156, A003157, A003158 are on page 500.] FORMULA a(n) = A079523(n) - n + 1 = A003157(n) - 2n = A003158(n) - 2n + 1. - Philippe Deléham, Feb 28 2004 a(n) = A036554(n) - n = A072939(n) - n - 1 = 2*A003159(n) - n. - Philippe Deléham, Apr 10 2004 a(n) = Sum_{k = 1..n} A080426(k). - Philippe Deléham, Apr 16 2004 MAPLE a:= proc(n) global l; while nops(l) [1, 3\$d, 1][], l) od; `if` (n=1, 1, a(n-1) +l[n]) end: l:= [1]: seq (a(n), n=1..80); # Alois P. Heinz, Oct 31 2009 MATHEMATICA Position[Nest[Flatten[# /. {0 -> {0, 2, 1}, 1 -> {0}, 2 -> {0}}]&, {0}, 7], 0] // Flatten (* Jean-François Alcover, Mar 14 2014 *) PROG (Haskell) following Deléham a003156 n = a003156_list !! (n-1) a003156_list = scanl1 (+) a080426_list -- Reinhard Zumkeller, Oct 27 2014 CROSSREFS Cf. A001511, A003157, A003158, A003159, A007413, A007913, A029883, A033485, A035263, A036554, A036585, A056196, A065882, A065883, A072939, A079523, A072939, A080426, A088172, A092412, A092606. See also A003144, A003145, A003146. Sequence in context: A047431 A288695 A182719 * A192360 A115984 A145025 Adjacent sequences: A003153 A003154 A003155 * A003157 A003158 A003159 KEYWORD nonn AUTHOR N. J. A. Sloane EXTENSIONS More terms from Alois P. Heinz, Oct 31 2009 Incorrect equation removed from formula by Peter Munn, Dec 11 2020 STATUS approved

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Last modified May 26 16:43 EDT 2024. Contains 372840 sequences. (Running on oeis4.)