A210496 Number of set partitions of [n] avoiding the patterns {1123, 1211}.

1, 1, 2, 5, 13, 33, 81, 196, 470, 1126, 2699, 6487, 15633, 37788, 91589, 222572, 542145, 1323446, 3237074, 7932108, 19469151, 47860083, 117819348, 290424126, 716772644, 1771035921, 4380646788, 10846386691, 26880759090, 66678169061, 165534924098, 411281773379, 1022621256416, 2544478797575, 6335428289930, 15784538365081, 39350771601502, 98158461390807

Offset

0,3

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

V. Jelinek, T. Mansour, M. Shattuck, On multiple pattern avoiding set partitions, Adv. Appl. Math. 50 (2) (2013) 292-326, Theorem 4.27.

Formula

G.f.: ( (1-x^2)*sqrt((1-x)*(1-x-4*x^2)) -(1-3*x-2*x^2 +14*x^3 -15*x^4 +3*x^5) / (1-x)^2 ) / ( 2*x^2*(1-3*x+x^2) ).

a(n) ~ sqrt((5389+1307*sqrt(17))/2)*((1+sqrt(17))/2)^n/(n^(3/2)*sqrt(Pi)). - Vaclav Kotesovec, Jul 30 2013

Conjecture: (n+2)*a(n) +2*(-3*n-4)*a(n-1) +4*(2*n+3)*a(n-2) +(13*n-40)*a(n-3) +5*(-7*n+18)*a(n-4) +6*(2*n-1)*a(n-5) +22*(n-7)*a(n-6) +(-19*n+134)*a(n-7) +2*(2*n-15)*a(n-8)=0. - R. J. Mathar, Oct 08 2016

Mathematica

CoefficientList[Series[((1-x^2)*Sqrt[(1-x)*(1-x-4*x^2)]-(1-3*x-2*x^2 +14*x^3-15*x^4+3*x^5)/(1-x)^2)/(2*x^2*(1-3*x+x^2)), {x, 0, 20}], x]

Prog

(PARI) x='x+O('x^50); Vec(( (1-x^2)*sqrt((1-x)*(1-x-4*x^2)) -(1-3*x-2*x^2+14*x^3-15*x^4+3*x^5) / (1-x)^2 ) / ( 2*x^2*(1-3*x+x^2) )) \\ G. C. Greubel, May 31 2017

Crossrefs

Sequence in context: A005183 A005348 A369578 * A067676 A292507 A307465

Adjacent sequences: A210493 A210494 A210495 * A210497 A210498 A210499

Keyword

nonn

Author

R. J. Mathar, Jan 25 2013

Extensions

Typo in g.f. corrected by Vaclav Kotesovec, Jul 30 2013

Status

approved