A092490 a(n) = A058094(n) - 3*A058094(n-1) + A058094(n-2) for n >=4.

0, 0, 0, 1, 5, 20, 75, 271, 957, 3337, 11559, 39896, 137423, 472808, 1625632, 5587228, 19198971, 65963978, 226623902, 778551761, 2674604282, 9188106871, 31563807424, 108430368827, 372487292867, 1279591674070, 4395730089428

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

• Colin Barker, Table of n, a(n) for n = 1..1000
• 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, A092491, A092492.

Cf. A058094.

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 32 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:for n from 4 to 32 do a[n]:=b[n]-3*b[n-1]+b[n-2] od: seq(a[n],n=1..32); # Emeric Deutsch, Apr 12 2005

PARI

concat([0,0,0], Vec(x^4*(1 - x + x^2 + x^3) / (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

G.f.: x^4*(1 - x + x^2 + x^3) / (1 - 6*x + 11*x^2 - 9*x^3 + 4*x^4 + 4*x^5 - x^6). - R. J. Mathar, Dec 02 2007

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>7. - Colin Barker, Aug 21 2019

Extensions

Edited by Emeric Deutsch, Apr 12 2005