A006328 Total preorders. (Formerly M3928)

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

3,1

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).

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)

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 *)

Prog

(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

Crossrefs

A column of A079502.

Sequence in context: A205669 A101147 A274723 * A213766 A000347 A270906

Adjacent sequences: A006325 A006326 A006327 * A006329 A006330 A006331

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

More terms from Sean A. Irvine, Mar 12 2017

Status

approved