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 A158005 Numbers of pattern-matching permutations of (1234) for the permutations of {1, 2, ..., n} on n = 4, 5, 6, ... elements. 142
 1, 17, 207, 2279, 24553, 268521, 3042210, 36153510, 454208895, 6059942223, 86030083110, 1299647574882, 20865826165777, 355277740280849, 6399391841784282, 121623163346687166, 2432739049821421911, 51089720946192154791, 1123991502048375026337 (list; graph; refs; listen; history; text; internal format)
 OFFSET 4,2 COMMENTS Same series for 1243 1432 2134 2143 4123 3214 3412 2341 3421 4321 4312. - R. H. Hardin, Mar 15 2009 LINKS Alois P. Heinz, Table of n, a(n) for n = 4..170 Eric Weisstein's World of Mathematics, Permutation Pattern FORMULA a(n) = A214152(n,4) = A000142(n) - A005802(n) = A000142(n) - A214015(n,3). - Alois P. Heinz, Jul 05 2012 MAPLE h:= proc(l) local n; n:=nops(l); add(i, i=l)!/mul(mul(1+l[i]-j +add(`if`(l[k]>=j, 1, 0), k=i+1..n), j=1..l[i]), i=1..n) end: g:= proc(n, i, l) `if`(n=0 or i=1, h([l[], 1\$n])^2, `if`(i<1, 0, add(g(n-i*j, i-1, [l[], i\$j]), j=0..n/i))) end: a:= n-> n! -g(n, 3, []): seq(a(n), n=4..30); # Alois P. Heinz, Jul 05 2012 # second Maple program a:= proc(n) option remember; `if`(n<3, 0, `if`(n=4, 1, ((13-11*n-40*n^2+10*n^3+n^4)*a(n-1) -(10*n^2-9*n-31)*(n-1)^2*a(n-2) +9*(n-1)^2*(n-2)^2*a(n-3)) / ((n-4)*(n+2)^2))) end: seq(a(n), n=4..30); # Alois P. Heinz, Sep 26 2012 MATHEMATICA a[2] = a[3] = 0; a[4] = 1; a[n_] := a[n] = (1/((n-4)*(n+2)^2))* (9*(n-2)^2*a[n-3]*(n-1)^2 - (10*n^2 - 9*n - 31)*a[n-2]*(n-1)^2 + (n^4 + 10*n^3 - 40*n^2 - 11*n + 13)*a[n-1]); Table[a[n], {n, 4, 22}] (* Jean-François Alcover, Oct 22 2012, after Alois P. Heinz *) CROSSREFS Cf. A000142, A005802, A214015, A214152. Sequence in context: A246989 A016981 A158009 * A158006 A239157 A014921 Adjacent sequences: A158002 A158003 A158004 * A158006 A158007 A158008 KEYWORD nonn AUTHOR Eric W. Weisstein, Mar 11 2009 EXTENSIONS More terms from R. H. Hardin, Mar 15 2009 Two more terms from Vladeta Jovovic, Aug 17 2009 Corrected a(19)-a(20) and extended by Alois P. Heinz, Jul 05 2012 STATUS approved

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Last modified December 4 10:17 EST 2023. Contains 367560 sequences. (Running on oeis4.)