A132647 - OEIS

%I #12 Feb 17 2024 08:40:56

%S 1,1,2,6,23,117,706,4962,39817,359171,3597936,39630372,476066277,

%T 6194080387,86776390796,1302376048620,20847721870931,354549730559949,

%U 6384006047649910,121330369923079290,2427196999663678987,50981866833670160201,1121806937829102793662

%N Number of permutations of [n] having no substring [k,k+1,k+2,k+3].

%H Andrew Howroyd, <a href="/A132647/b132647.txt">Table of n, a(n) for n = 0..200</a>

%H D. M. Jackson and R. C. Read, <a href="http://gdz.sub.uni-goettingen.de/dms/load/img/?PID=GDZPPN002031183">A note on permutations without runs of given length</a>, Aequationes Math. 17 (1978), no. 2-3, 336-343.

%F G.f.: Sum_{n>=0} n!*((x^m-x)/(x^m-1))^n where m = 4.

%F a(n) ~ n! * (1 - 1/n^2 + 1/n^3 + 9/(2*n^4) + 7/n^5 - 55/(6*n^6) - 114/n^7 - 11419/(24*n^8) - 970/n^9 + 345199/(120*n^10) + ...). - _Vaclav Kotesovec_, Feb 17 2024

%o (PARI) seq(n)={Vec(sum(k=0, n, k!*((x^4-x)/(x^4-1) + O(x*x^n))^k))} \\ _Andrew Howroyd_, Aug 31 2018

%Y Cf. A000255, A002628.

%K nonn

%O 0,3

%A Ivana Jovovic (ivana121(AT)EUnet.yu), Nov 14 2007

%E Terms a(16) and beyond from _Andrew Howroyd_, Aug 31 2018