A092491 a(n) = 2*A058094(n-2) - 5*A058094(n-3) + A058094(n-4) + a(n-1) for n >=4.

0, 0, 0, 0, 1, 6, 25, 93, 333, 1172, 4083, 14137, 48778, 167981, 577874, 1986747, 6828120, 23462470, 80611581, 276944893, 951422603, 3268470411, 11228209786, 38572124196, 132505812826, 455192771711, 1563706508759, 5371738013650

Offset: 1

Author

N. J. A. Sloane, Apr 04 2004

Keywords

• nonn
• easy

Comments

A recurrence relation follows in a straightforward manner from the above formula and the recurrence relation for A058094.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..200
• Z. Stankova and J. West, Explicit enumeration of 321, hexagon-avoiding permutations, Discrete Math., 280 (2004), 165-189.
• Index entries for linear recurrences with constant coefficients, signature (6,-11,9,-4,-4,1).

Crossrefs

Cf. A058094, A092489, A092490, A092492.

Programs

Maple

b[1]:=1:b[2]:=2:b[3]:=5:b[4]:=14:b[5]:=42:b[6]:=132: for n from 6 to 34 do b[n+1]:=6*b[n]-11*b[n-1]+9*b[n-2]-4*b[n-3]-4*b[n-4]+b[n-5] od: a[1]:=0:a[2]:=0:a[3]:=0:a[4]:=0: for n from 5 to 34 do a[n]:=2*b[n-2]-5*b[n-3]+b[n-4]+a[n-1] od: seq(a[n],n=1..34); # Emeric Deutsch, Apr 12 2005

Mathematica

LinearRecurrence[{6, -11, 9, -4, -4, 1}, {0, 0, 0, 0, 1, 6}, 40] (* Vincenzo Librandi, Aug 15 2017 *)

PARI

concat([0,0,0,0], Vec(x^5 / (1 - 6*x + 11*x^2 - 9*x^3 + 4*x^4 + 4*x^5 - x^6) + O(x^30))) \\ Colin Barker, Aug 21 2019

Formula

From Colin Barker, Aug 21 2019: (Start)

G.f.: x^5 / (1 - 6*x + 11*x^2 - 9*x^3 + 4*x^4 + 4*x^5 - x^6).

a(n) = 6*a(n-1) - 11*a(n-2) + 9*a(n-3) - 4*a(n-4) - 4*a(n-5) + a(n-6) for n>6.

(End)

Extensions

Edited by Emeric Deutsch, Apr 12 2005