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A289657 Number of 3-abelian equivalence classes of words of length n over a binary alphabet. 2
1, 2, 4, 8, 16, 32, 60, 106, 176, 280, 426, 626, 892, 1238, 1678, 2230, 2910, 3738, 4734, 5920, 7318, 8954, 10852, 13040, 15546, 18400, 21632, 25276, 29364, 33932, 39016, 44654, 50884, 57748, 65286, 73542, 82560, 92386, 103066, 114650, 127186, 140726, 155322, 171028, 187898, 205990, 225360, 246068 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Ray Chandler, Table of n, a(n) for n = 0..1000

Julien Cassaigne, J. Karhumäki, S. Puzynina, M. A. Whiteland, k-Abelian Equivalence and Rationality, in International Conference on Developments in Language Theory DLT 2016: Developments in Language Theory pp 77-88, Lecture Notes in Computer Science book series (LNCS, volume 9840).

Julien Cassaigne, Juhani Karhumaki, Svetlana Puzynina, Markus A. Whiteland, k-Abelian Equivalence and Rationality, Fundamenta Informaticae 154 (2017) 1-30, DOI 10.3233/FI-2017-1531.

Juhani Karhumäki, Markus A. Whiteland, Regularity of k-Abelian Equivalence Classes of Fixed Cardinality, Adventures Between Lower Bounds and Higher Altitudes, Lecture Notes in Computer Science, Vol. 11011, Springer, Cham, 49-62.

Index entries for linear recurrences with constant coefficients, signature (3, -2, -1, 0, 1, 2, -3, 1).

FORMULA

See Maple code.

G.f.: (1 - x + x^3 + 2*x^4 + 3*x^5 + x^7 - x^8 + 2*x^9) / ((1 - x)^5*(1 + x)*(1 + x + x^2)). - Colin Barker, Jul 23 2017

MAPLE

# This is for n >= 2:

P32:=proc(n) local t1, c, w; c:=exp(Pi*I/3); w:=c^2;

t1:=n^4/18-5*n^3/18+65*n^2/36-23*n/6-(-1)^n/8

+(2/27)*(w^n/c+c/w^n)+1307/216;

round(Re(evalf(simplify(t1))));

end;

[seq(P32(n), n=2..56)];

MATHEMATICA

CoefficientList[Series[(1 - x + x^3 + 2 x^4 + 3 x^5 + x^7 - x^8 + 2 x^9)/((1 - x)^5*(1 + x) (1 + x + x^2)), {x, 0, 47}], x] (* Michael De Vlieger, Nov 29 2018 *)

PROG

(PARI) Vec((1 - x + x^3 + 2*x^4 + 3*x^5 + x^7 - x^8 + 2*x^9) / ((1 - x)^5*(1 + x)*(1 + x + x^2)) + O(x^50)) \\ Colin Barker, Jul 24 2017

CROSSREFS

Cf. A289658.

Sequence in context: A196724 A056644 A007813 * A005309 A078389 A248847

Adjacent sequences:  A289654 A289655 A289656 * A289658 A289659 A289660

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, Jul 22 2017

STATUS

approved

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Last modified November 20 13:24 EST 2019. Contains 329336 sequences. (Running on oeis4.)