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A002630
Number of permutations of length n with two 3-sequences.
(Formerly M2032 N0804)
2
0, 0, 0, 1, 2, 12, 71, 481, 3708, 32028, 306723, 3228804, 37080394, 461569226, 6192527700, 89102492915, 1369014167140, 22373840093040, 387602212164321, 7095737193164187, 136885937242792752, 2775675888994318366, 59023506305591628101, 1313445236142071926488
OFFSET
1,5
REFERENCES
D. M. Jackson, J. W. Reilly, Permutations with a prescribed number of $p$-runs. Ars Combinatoria 1 (1976), no. 1, 297-305.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
J. Riordan, Permutations without 3-sequences, Bull. Amer. Math. Soc., 51 (1945), 745-748.
MATHEMATICA
nmax = 22;
CoefficientList[Sum[((m + 2)*(m + 1)*(m + 2)!/2*(x^6*(1 - x)^4/(1 - x^3)^4) + (m + 1)*(m + 1)!*(x^4*(1 + x)*(1 - x)^3)/(1 - x^3)^3)*((x - x^3)/(1 - x^3))^m, {m, 0, nmax}]/x + O[x]^nmax, x] (* Jean-François Alcover, May 06 2024, after Tani Akinari *)
PROG
(PARI) concat([0, 0, 0], Vec(sum(m=0, 100, ((m+2)*(m+1)*(m+2)!/2*(x^6*(1-x)^4/(1-x^3)^4)+(m+1)*(m+1)!*(x^4*(1+x)*(1-x)^3)/(1-x^3)^3)*((x-x^3)/(1-x^3))^m)+O(x^100))) \\ Tani Akinari, Nov 08 2014
CROSSREFS
Cf. A047921.
Sequence in context: A012376 A223763 A361960 * A009552 A002670 A119921
KEYWORD
nonn
EXTENSIONS
More terms from Max Alekseyev, Feb 20 2010
STATUS
approved