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 A190830 Number of permutations of 4 copies of 1..n introduced in order 1..n with no element equal to another within a distance of 1. 9
 1, 0, 1, 182, 94376, 98371884, 182502973885, 551248360550999, 2536823683737613858, 16904301142107043464659, 156690501089429126239232946, 1955972150994131850032960933480, 32016987304767134806200915633253966, 672058204939482014438623912695190927357 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 LINKS Seiichi Manyama, Table of n, a(n) for n = 0..158 (terms 1..28 from R. J. Mathar) R. J. Mathar, A class of multinomial permutations avoiding object clusters, vixra:1511.0015 (2015), sequence M_{c,4}/c!. FORMULA From Vaclav Kotesovec, Nov 24 2018: (Start) Recurrence: 3*(64*n^3 - 280*n^2 + 414*n - 245)*a(n) = (2048*n^6 - 12032*n^5 + 30400*n^4 - 42608*n^3 + 32484*n^2 - 14624*n + 1731)*a(n-1) + 3*(3840*n^5 - 20640*n^4 + 40104*n^3 - 36340*n^2 + 23378*n - 13429)*a(n-2) - 18*(384*n^4 - 1488*n^3 + 1556*n^2 - 986*n + 649)*a(n-3) - 27*(64*n^3 - 88*n^2 + 46*n - 47)*a(n-4). a(n) ~ 2^(5*n+1) * n^(3*n) / (3^n * exp(3*n + 3)). (End) EXAMPLE Some solutions for n=3: 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 1 3 3 1 3 3 3 3 3 3 1 1 3 1 1 1 2 2 2 2 2 2 1 1 2 1 3 3 1 3 2 2 3 3 3 1 1 3 2 2 3 2 1 2 3 1 1 3 2 1 2 3 2 1 3 1 1 3 2 3 2 2 3 1 3 2 3 2 3 3 1 3 2 2 3 2 1 3 1 3 2 3 1 3 1 2 3 1 1 1 2 1 3 2 3 1 1 1 3 1 3 1 2 2 3 3 3 2 2 3 2 2 3 2 1 3 2 3 1 3 1 1 2 3 3 1 3 3 1 1 2 2 3 1 3 2 2 2 3 1 1 3 2 2 3 3 1 3 1 2 2 3 3 3 1 3 2 2 3 CROSSREFS Row n=4 of A322013. Cf. A190826, A321633. Sequence in context: A225712 A371805 A015306 * A145525 A028676 A228535 Adjacent sequences: A190827 A190828 A190829 * A190831 A190832 A190833 KEYWORD nonn AUTHOR R. H. Hardin, May 21 2011 EXTENSIONS a(0)=1 prepended by Seiichi Manyama, Nov 16 2018 STATUS approved

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Last modified July 25 05:51 EDT 2024. Contains 374586 sequences. (Running on oeis4.)