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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 (list; graph; refs; listen; history; text; internal format)
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

Table of n, a(n) for n=1..22.

J. Riordan, Permutations without 3-sequences, Bull. Amer. Math. Soc., 51 (1945), 745-748.

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: A012381 A012376 A223763 * A009552 A002670 A119921

Adjacent sequences:  A002627 A002628 A002629 * A002631 A002632 A002633

KEYWORD

nonn

AUTHOR

N. J. A. Sloane

EXTENSIONS

More terms from Max Alekseyev, Feb 20 2010

STATUS

approved

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Last modified October 23 20:01 EDT 2019. Contains 328373 sequences. (Running on oeis4.)