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 A332783 The number of permutations of {(n+1) 1's, (n+1) 2's, ..., (n+1) n's} with the property that k's are equally spaced for k=1..n and the interval of k+1 is less than or equal to the interval of k for k=1..n-1. 5
 1, 4, 16, 104, 484, 4848, 25104, 300336, 2335296, 27953952, 198725952, 4731323904, 33020828928, 606237831936, 8936541384192, 174694058933760, 1628654065588224, 56338295740213248, 545177455792662528, 20766878061520306176, 340162958990367645696 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Table of n, a(n) for n=1..21. EXAMPLE Define the interval of k as b(k). In case of n = 1. | | b(1) -----+--------+----- 1 | [1, 1] | [0] In case of n = 2. | | b(1),b(2) -----+--------------------+---------- 1 | [2, 2, 2, 1, 1, 1] | [0, 0] 2 | [2, 1, 2, 1, 2, 1] | [1, 1] 3 | [1, 2, 1, 2, 1, 2] | [1, 1] 4 | [1, 1, 1, 2, 2, 2] | [0, 0] In case of n = 3. | | b(1),b(2),b(3) -----+--------------------------------------+--------------- 1 | [3, 3, 3, 3, 2, 2, 2, 2, 1, 1, 1, 1] | [0, 0, 0] 2 | [3, 3, 3, 3, 2, 1, 2, 1, 2, 1, 2, 1] | [1, 1, 0] 3 | [3, 3, 3, 3, 1, 2, 1, 2, 1, 2, 1, 2] | [1, 1, 0] 4 | [3, 3, 3, 3, 1, 1, 1, 1, 2, 2, 2, 2] | [0, 0, 0] 5 | [3, 2, 1, 3, 2, 1, 3, 2, 1, 3, 2, 1] | [2, 2, 2] 6 | [3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2] | [2, 2, 2] 7 | [2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1] | [2, 2, 2] 8 | [1, 3, 2, 1, 3, 2, 1, 3, 2, 1, 3, 2] | [2, 2, 2] 9 | [2, 1, 3, 2, 1, 3, 2, 1, 3, 2, 1, 3] | [2, 2, 2] 10 | [1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3] | [2, 2, 2] 11 | [2, 2, 2, 2, 3, 3, 3, 3, 1, 1, 1, 1] | [0, 0, 0] 12 | [1, 1, 1, 1, 3, 3, 3, 3, 2, 2, 2, 2] | [0, 0, 0] 13 | [2, 2, 2, 2, 1, 1, 1, 1, 3, 3, 3, 3] | [0, 0, 0] 14 | [2, 1, 2, 1, 2, 1, 2, 1, 3, 3, 3, 3] | [1, 1, 0] 15 | [1, 2, 1, 2, 1, 2, 1, 2, 3, 3, 3, 3] | [1, 1, 0] 16 | [1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3] | [0, 0, 0] PROG (Ruby) def search(a, num, d, k, n) if num == 0 @cnt += 1 else (k * n - k + 1).times{|i| if a[i] == 0 (i + d + 1..k * n - k + 1).each{|j| if (k - 1) * j - (k - 2) * i < k * n if (1..k - 1).all?{|m| a[m * j - (m - 1) * i] == 0} (0..k - 1).each{|m| a[m * j - (m - 1) * i] = num} search(a, num - 1, j - i - 1, k, n) (0..k - 1).each{|m| a[m * j - (m - 1) * i] = 0} end end } end } end end def A(k, n) a = [0] * k * n @cnt = 0 search(a, n, 0, k, n) @cnt end def A332783(n) (1..n).map{|i| A(i + 1, i)} end p A332783(5) CROSSREFS Cf. A104442, A332762, A332784, A322178, A332748, A332752, A332773. Sequence in context: A245155 A334750 A094637 * A332773 A203716 A330537 Adjacent sequences: A332780 A332781 A332782 * A332784 A332785 A332786 KEYWORD nonn AUTHOR Seiichi Manyama, Feb 23 2020 EXTENSIONS a(9)-a(17) from Bert Dobbelaere, Mar 08 2020 a(18)-a(21) from Max Alekseyev, Sep 26 2023 STATUS approved

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Last modified November 30 02:55 EST 2023. Contains 367452 sequences. (Running on oeis4.)