This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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. - R. J. Mathar, Dec 11 2008 LINKS E. Barcucci et al., From Motzkin to Catalan Permutations, Discr. Math., 217 (2000), 33-49. Nickolas Hein, Jia Huang, Variations of the Catalan numbers from some nonassociative binary operations, arXiv:1807.04623 [math.CO], 2018. 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 + ... MATHEMATICA a[0] = 1; a[n_] := Module[{M}, M = Table[If[j < i || i == j && i <= 4 || j == i+1, 1, 0], {i, 1, n}, {j, 1, n}]; MatrixPower[M, n][[1, 1]]]; Table[a[n], {n, 0, 26}] (* Jean-François Alcover, Aug 16 2018, after A054391 *) 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: A290134 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified October 15 21:17 EDT 2019. Contains 328038 sequences. (Running on oeis4.)