A006328 Total preorders.

5, 24, 79, 223, 579, 1432, 3434, 8071, 18714, 42991, 98127, 222965, 505008, 1141236, 2574845, 5802636, 13065935, 29403439, 66141015, 148734156, 334391354, 751675943, 1689494650, 3797059555, 8533209055, 19176039925, 43091557504, 96831330948, 217586892705

Offset: 3

Author

N. J. A. Sloane

Keywords

• nonn
• easy

References

• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• Colin Barker, Table of n, a(n) for n = 3..1000
• G. Kreweras, Les préordres totaux compatibles avec un ordre partiel, Math. Sci. Humaines No. 53 (1976), 5-30.
• G. Kreweras, Les préordres totaux compatibles avec un ordre partiel, Math. Sci. Humaines No. 53 (1976), 5-30. (Annotated scanned copy)
• Index entries for linear recurrences with constant coefficients, signature (4,-3,-4,4,1,-1).

Crossrefs

A column of A079502.

Programs

Mathematica

CoefficientList[ Series[(5 + 4x - 2x^2 - x^3)/(1 - 4x + 3x^2 + 4x^3 - 4 x^4 - x^5 + x^6), {x, 0, 30}], x] (* Robert G. Wilson v, Mar 12 2017 *)

PARI

Vec(x^3*(1 + x)*(5 - x - x^2) / ((1 - x)*(1 - x - x^2)*(1 - 2*x - x^2 + x^3)) + O(x^40)) \\ Colin Barker, Mar 19 2017

Formula

From Colin Barker, Mar 19 2017: (Start)

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

a(n) = 4*a(n-1) - 3*a(n-2) - 4*a(n-3) + 4*a(n-4) + a(n-5) - a(n-6) for n>8.

(End)

Extensions

More terms from Sean A. Irvine, Mar 12 2017