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 A004738 Concatenation of sequences (1,2,...,n-1,n,n-1,...,2) for n >= 2. 12
 1, 2, 1, 2, 3, 2, 1, 2, 3, 4, 3, 2, 1, 2, 3, 4, 5, 4, 3, 2, 1, 2, 3, 4, 5, 6, 5, 4, 3, 2, 1, 2, 3, 4, 5, 6, 7, 6, 5, 4, 3, 2, 1, 2, 3, 4, 5, 6, 7, 8, 7, 6, 5, 4, 3, 2, 1, 2, 3, 4, 5, 6, 7, 8, 9, 8, 7, 6, 5, 4, 3, 2, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 10, 9 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Also concatenation of sequences n,n-1,...,2,1,2,...,n-1,n. Table T(n,k) n, k > 0, T(n,k) = n-k+1, if n >= k, T(n,k) = k-n+1, if n < k.  Table read by sides of squares from T(1,n) to T(n,n), then from T(n,n) to T(n,1). General case A209301. Let m be a natural number. The first column of the table T(n,1) is the sequence of the natural numbers A000027. In all columns with number k (k > 1) the segment with the length of (k-1): {m+k-2, m+k-3, ..., m} shifts the sequence A000027. For m=1 the result is A004739, for m=2 the result is A004738, for m=3 the result is A209301. - Boris Putievskiy, Jan 24 2013 REFERENCES F. Smarandache, "Numerical Sequences", University of Craiova, 1975; [ See Arizona State University, Special Collection, Tempe, AZ, USA ]. LINKS Boris Putievskiy, Transformations [Of] Integer Sequences And Pairing Functions, arXiv preprint arXiv:1212.2732 [math.CO], 2012. F. Smarandache, Collected Papers, Vol. II F. Smarandache, Sequences of Numbers Involved in Unsolved Problems. Eric Weisstein's World of Mathematics, Smarandache Sequences FORMULA a(n) = floor(sqrt(n) + 1/2) + 1 - abs(n - 1 - (floor(sqrt(n) + 1/2))^2). - Benoit Cloitre, Feb 08 2003 From Boris Putievskiy, Jan 24 2013: (Start) For the general case, a(n) = m*v + (2*v-1)*(t*t-n) + t, where t = floor((sqrt(n) - 1/2) + 1 and v = floor((n-1)/t) - t + 1. For m=2, a(n) = 2*v + (2*v-1)*(t*t-n)+t, where t = floor((sqrt(n) - 1/2) + 1 and v = floor((n-1)/t) - t + 1. (End) EXAMPLE From Boris Putievskiy, Jan 24 2013: (Start) The start of the sequence as table:   1, 2, 3, 4, 5, 6, 7, ...   2, 1, 2, 3, 4, 5, 6, ...   3, 2, 1, 2, 3, 4, 5, ...   4, 3, 2, 1, 2, 3, 4, ...   5, 4, 3, 2, 1, 2, 3, ...   6, 5, 4, 3, 2, 1, 2, ...   7, 6, 5, 4, 3, 2, 1, ...   ... The start of the sequence as triangle array read by rows:   1;   2, 1, 2;   3, 2, 1, 2, 3;   4, 3, 2, 1, 2, 3, 4;   5, 4, 3, 2, 1, 2, 3, 4, 5;   6, 5, 4, 3, 2, 1, 2, 3, 4, 5, 6;   7, 6, 5, 4, 3, 2, 1, 2, 3, 4, 5, 6, 7;   ... Row number r contains 2*r - 1 numbers: r, r-1, ..., 1, 2, ..., r. (End) MAPLE A004738 := proc(n)     local tri ;     tri := floor(sqrt(n)+1/2) ;     tri+1-abs(n-1-tri^2) ; end proc: seq(A004738(n), n=1..30) ; #R. J. Mathar, Feb 14 2019 MATHEMATICA row[n_] := Range[n, 1, -1] ~Join~ Range[2, n]; Array[row, 10] // Flatten (* Jean-François Alcover, Apr 19 2020 *) PROG (PARI) a(n)= floor(sqrt(n)+1/2)+1-abs(n-1-(floor(sqrt(n)+1/2)-1/2)^2) CROSSREFS Cf. A004737, A004739, A187760, A079813, A209301. Sequence in context: A088696 A257249 A267108 * A043554 A005811 A008342 Adjacent sequences:  A004735 A004736 A004737 * A004739 A004740 A004741 KEYWORD nonn,easy AUTHOR R. Muller EXTENSIONS More terms from Patrick De Geest, Jun 15 1998 STATUS approved

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Last modified August 3 11:47 EDT 2021. Contains 346435 sequences. (Running on oeis4.)