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 A048328 Numbers that are repdigits in base 3. 10
 0, 1, 2, 4, 8, 13, 26, 40, 80, 121, 242, 364, 728, 1093, 2186, 3280, 6560, 9841, 19682, 29524, 59048, 88573, 177146, 265720, 531440, 797161, 1594322, 2391484, 4782968, 7174453, 14348906, 21523360, 43046720, 64570081, 129140162, 193710244, 387420488, 581130733 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Case for base 2 see A000225: 2^n - 1. If the sequence b(n) represents the number of paths of length n, n >= 1, starting at node 1 and ending at nodes 1, 2, 3 and 4 on the path graph P_5 then a(n-1) = b(n) - 1. - Johannes W. Meijer, May 29 2010 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..1000 Eric Weisstein's World of Mathematics, Repdigit. Index entries for 3-automatic sequences. Index entries for linear recurrences with constant coefficients, signature (0,4,0,-3). FORMULA G.f.: (2*x^2+x)/(1-4*x^2+3*x^4). - Alois P. Heinz, Sep 23 2012 Sum_{n>=1} 1/a(n) = 3 * A214369 = 2.04646050781571420028... - Amiram Eldar, Jan 21 2022 a(n) = (3^(n/2)*(sqrt(3) + 2 - (-1)^n*(sqrt(3) - 2)) - 3 - (-1)^n)/4. - Stefano Spezia, Feb 18 2022 MAPLE nmax := 35; a(0) := 0: for n from 1 to nmax do a(2*n) := a(2*n-2) + 2*3^(n-1); od: a(1) := 1: for n from 1 to nmax do a(2*n+1) := 1*a(2*n-1) + 3^n; od: seq(a(n), n=0..nmax); # End program 1 with(GraphTheory): G := PathGraph(5): A:= AdjacencyMatrix(G): nmax := nmax; for n from 1 to nmax+1 do B(n) := A^n; b(n) := add(B(n)[1, k], k=1..4); a1(n-1) := b(n)-1; od: seq(a1(n), n=0..nmax); # End program 2 # From Johannes W. Meijer, May 29 2010, revised Sep 23 2012 # third Maple program: a:= n->(<<0|1>, <-3|4>>^iquo(n, 2, 'r').`if`(r=0, <<0, 2>>, <<1, 4>>))[1, 1]: seq (a(n), n=0..60); # Alois P. Heinz, Sep 23 2012 MATHEMATICA Rest[FromDigits[#, 3]&/@Flatten[Table[{PadRight[{1}, n, 1], PadRight[{2}, n, 2]}, {n, 0, 20}], 1]] (* Harvey P. Dale, Feb 03 2011 *) PROG (PARI) a(n)=([0, 1, 0, 0; 0, 0, 1, 0; 0, 0, 0, 1; -3, 0, 4, 0]^n*[0; 1; 2; 4])[1, 1] \\ Charles R Greathouse IV, Oct 07 2015 CROSSREFS Bisections: A024023 and A003462. Cf. A000225, A010785, A028987, A028988, A033016, A038754, A068911, A124302, A214369. Sequence in context: A043799 A043807 A043816 * A094767 A263292 A026643 Adjacent sequences: A048325 A048326 A048327 * A048329 A048330 A048331 KEYWORD nonn,base,easy AUTHOR Patrick De Geest, Feb 15 1999 STATUS approved

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Last modified July 19 13:57 EDT 2024. Contains 374394 sequences. (Running on oeis4.)