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 A022856 a(n) = n-2 + Sum_{i = 1..n-2} (a(i+1) mod a(i)) for n >= 3 with a(1) = a(2) = 1. 18
 1, 1, 1, 2, 3, 5, 8, 12, 17, 23, 30, 38, 47, 57, 68, 80, 93, 107, 122, 138, 155, 173, 192, 212, 233, 255, 278, 302, 327, 353, 380, 408, 437, 467, 498, 530, 563, 597, 632, 668, 705, 743, 782, 822, 863, 905, 948, 992, 1037, 1083, 1130, 1178, 1227 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS Essentially triangular numbers + 2, but with three extra initial terms. LINKS G. C. Greubel, Table of n, a(n) for n = 1..5000 Guo-Niu Han, Enumeration of Standard Puzzles, 2011. [Cached copy] Guo-Niu Han, Enumeration of Standard Puzzles, arXiv:2006.14070 [math.CO], 2020. Index entries for linear recurrences with constant coefficients, signature (3,-3,1). FORMULA For n > 3, a(n) = (n^2 - 7*n + 16)/2 = A027689(n-4)/2 = A000217(n-4) + 2 = A000124(n-4) + 1. - Henry Bottomley, Jun 27 2000 a(n) = Sum_{k=0..2} A007318(n-k-2, k) for n > 3. - Johannes W. Meijer, Aug 11 2013 Sum_{n>=1} 1/a(n) = 3 + 2*Pi*tanh(sqrt(15)*Pi/2)/sqrt(15). - Amiram Eldar, Dec 13 2022 MATHEMATICA a[n_] := If[n<4, 1, (n^2-7n+16)/2]; Array[a, 60] (* Jean-François Alcover, Mar 08 2017 *) PROG (PARI) for(n=1, 100, print1(if(n<4, 1, (n^2 - 7*n +16)/2), ", ")) \\ G. C. Greubel, Jul 13 2017 CROSSREFS Cf. A000124, A000217, A007318, A027689. Sequence in context: A104664 A338921 A333343 * A089071 A177205 A275580 Adjacent sequences: A022853 A022854 A022855 * A022857 A022858 A022859 KEYWORD nonn,easy AUTHOR Clark Kimberling STATUS approved

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Last modified July 20 15:46 EDT 2024. Contains 374459 sequences. (Running on oeis4.)