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 A061579 Reverse one number (0), then two numbers (2,1), then three (5,4,3), then four (9,8,7,6), etc. 18
 0, 2, 1, 5, 4, 3, 9, 8, 7, 6, 14, 13, 12, 11, 10, 20, 19, 18, 17, 16, 15, 27, 26, 25, 24, 23, 22, 21, 35, 34, 33, 32, 31, 30, 29, 28, 44, 43, 42, 41, 40, 39, 38, 37, 36, 54, 53, 52, 51, 50, 49, 48, 47, 46, 45, 65, 64, 63, 62, 61, 60, 59, 58, 57, 56, 55, 77, 76, 75, 74, 73, 72 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS A self-inverse permutation of the nonnegative numbers. a(n) is the smallest nonnegative integer not yet in the sequence such that n + a(n) is one less than a square. [Franklin T. Adams-Watters, Apr 06 2009] From Michel Marcus, Mar 01 2021: (Start) Array T(n,k) = (n+k)^2/2 + (n+3*k)/2 for n,k >=0 read by descending antidiagonals. Array T(n,k) = (n+k)^2/2 + (3*n+k)/2 for n,k >=0 read by ascending antidiagonals. (End) LINKS Harry J. Smith, Table of n, a(n) for n = 0..1000 Madeline Brandt and Kåre Schou Gjaldbæk, Classification of Quadratic Packing Polynomials on Sectors of R^2, arXiv:2102.13578 [math.NT], 2021. See Figure 9 p. 17. FORMULA a(n) = floor(sqrt(2n+1)-1/2)*floor(sqrt(2n+1)+3/2) - n = A005563(A003056(n)) - n. Row (or antidiagonal) n = 0, 1, 2, ... contains the integers from A000217(n) to A000217(n+1)-1 in reverse order (for diagonals, "reversed" with respect to the canonical "falling" order, cf. A001477/table). - M. F. Hasler, Nov 09 2021 EXAMPLE Read as a triangle, the sequence is:     0     2   1     5   4   3     9   8   7   6    14  13  12  11  10   (...) As an infinite square matrix (cf. the "table" link, 2nd paragraph) it reads:     0    2    5    9   14   20   ...     1    4    8   13   19   22   ...     3    7   12   18   23   30   ...     6   11   17   24   31   39   ...   (...) MATHEMATICA Module[{nn=20}, Reverse/@TakeList[Range[0, (nn(nn+1))/2], Range[nn]]]// Flatten (* Requires Mathematica version 11 or later *) (* Harvey P. Dale, Jul 06 2018 *) PROG (PARI) A061579_row(n)=vector(n+=1, j, n*(n+1)\2-j) A061579_upto(n)=concat([A061579_row(r)|r<-[0..sqrtint(2*n)]]) \\ yields approximately n terms: actual number differs by less than +- sqrt(n). - M. F. Hasler, Nov 09 2021 CROSSREFS Fixed points are A046092. Each reversal involves the numbers from A000217 through to A000096. Cf. A038722. Transpose of A001477. Sequence in context: A275131 A280513 A185023 * A094064 A343809 A159930 Adjacent sequences:  A061576 A061577 A061578 * A061580 A061581 A061582 KEYWORD nonn,tabl AUTHOR Henry Bottomley, May 21 2001 STATUS approved

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Last modified October 3 22:17 EDT 2022. Contains 357237 sequences. (Running on oeis4.)