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A054392 Number of permutations with certain forbidden subsequences. 3
1, 1, 2, 5, 14, 42, 131, 418, 1352, 4410, 14463, 47605, 157084, 519255, 1718653, 5693903, 18877509, 62620857, 207816230, 689899944, 2290913666, 7608939443, 25276349558, 83977959853, 279039638062, 927272169336, 3081641953082 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Apparently the Motzkin transform of A005251, after A005251(0) is set to 1. [From R. J. Mathar, Dec 11 2008]

LINKS

Table of n, a(n) for n=0..26.

E. Barcucci et al., From Motzkin to Catalan Permutations, Discr. Math., 217 (2000), 33-49.

FORMULA

Conjecture: (-n+2)*a(n) +(8*n-19)*a(n-1) +(-20*n+49)*a(n-2) +(11*n-1)*a(n-3) +(19*n-116)*a(n-4) +21*(-n+5)*a(n-5)=0. - R. J. Mathar, Aug 09 2015

EXAMPLE

G.f. = 1 + x + 2*x^2 + 5*x^3 + 14*x^4 + 42*x^5 + 131*x^6 + 418*x^7 + 1352*x^8 + ...

PROG

(PARI) {a(n) = if( n<1, n==0, polcoeff( subst( x * (1 - x) / (1 - 2*x + x^2 - x^3), x, serreverse( x / (1 + x + x^2) + x * O(x^n))), n))}; /* Michael Somos, Aug 06 2014 */

CROSSREFS

Interpolates between Motzkin numbers (A001006) and Catalan numbers (A000108). Cf. A005773, A054391-A054394.

Sequence in context: A148328 A080937 A196417 * A261588 A006930 A036767

Adjacent sequences:  A054389 A054390 A054391 * A054393 A054394 A054395

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Elisa Pergola (elisa(AT)dsi.unifi.it), May 21 2000

STATUS

approved

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Last modified December 7 23:55 EST 2016. Contains 278902 sequences.