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A005943 Number of subwords of length n in the Golay-Rudin-Shapiro binary word A020987.
(Formerly M1116)
3
1, 2, 4, 8, 16, 24, 36, 46, 56, 64, 72, 80, 88, 96, 104, 112, 120, 128, 136, 144, 152, 160, 168, 176, 184, 192, 200, 208, 216, 224, 232, 240, 248, 256, 264, 272, 280 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Terms a(0)..a(13) verified and a(14)..a(32) computed using the first 2^32 terms of the GRS sequence. [Joerg Arndt, Jun 10 2012]

Terms a(0)..a(63) computed using the first 2^36 terms of the GRS sequence consistent with Arndt's conjectured g.f. - Sean A. Irvine, Oct 12 2016

REFERENCES

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

LINKS

Table of n, a(n) for n=0..36.

J.-P. Allouche and J. Shallit, The ring of k-regular sequences, Theoretical Computer Sci., 98 (1992), 163-197.

FORMULA

Conjectured g.f. (1+x^2+2*x^3+4*x^4+4*x^6-2*x^7-2*x^9)/(1-x)^2. [Joerg Arndt, Jun 10 2012]

EXAMPLE

All 8 subwords of length three (000, 001, ..., 111) occur in A020987, so a(3) = 8.

MATHEMATICA

CoefficientList[ Series[ (1 + x^2 + 2*x^3 + 4*x^4 + 4*x^6 - 2*x^7 - 2*x^9) / (1-x)^2, {x, 0, 36}], x] (* Jean-Fran├žois Alcover, Jan 10 2013, after Joerg Arndt's conjectured g.f. *)

CROSSREFS

Cf. A006697, A005942.

Sequence in context: A072874 A160158 A010072 * A008233 A224815 A031923

Adjacent sequences:  A005940 A005941 A005942 * A005944 A005945 A005946

KEYWORD

nonn,nice,more

AUTHOR

N. J. A. Sloane, Jeffrey Shallit.

EXTENSIONS

Minor edits by N. J. A. Sloane, Jun 06 2012

Added a(14)-a(32), Joerg Arndt, Jun 10 2012.

Added a(33)-a(36), Joerg Arndt, Oct 28 2012.

STATUS

approved

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Last modified March 28 02:14 EDT 2017. Contains 284182 sequences.