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A062258 Number of (0,1)-strings of length n not containing the substring 0100100. 2
1, 2, 4, 8, 16, 32, 64, 127, 252, 500, 993, 1972, 3916, 7776, 15441, 30662, 60887, 120906, 240088, 476753, 946709, 1879921, 3733040, 7412858, 14720031, 29230199, 58043664, 115259801, 228876346, 454489608, 902499570, 1792132228 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Also, number of (0,1)-strings of length n not containing the substring 1001001. - N. J. A. Sloane, Apr 02 2012

REFERENCES

I. P. Goulden and D. M. Jackson, Combinatorial Enumeration, Wiley, N.Y., 1983, (Problem 2.8.2).

Reilly, J. W.; Stanton, R. G. Variable strings with a fixed substring. Proceedings of the Second Louisiana Conference on Combinatorics, Graph Theory and Computing (Louisiana State Univ., Baton Rouge, La., 1971), pp. 483--494. Louisiana State Univ., Baton Rouge, La.,1971. MR0319775 (47 #8317) [From N. J. A. Sloane, Apr 02 2012]

LINKS

Table of n, a(n) for n=0..31.

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

FORMULA

G.f.: (1 + x^3 + x^6)/(1 - 2*x + x^3 - 2*x^4 + x^6 - x^7).

a(n) = 2*a(n-1) - a(n-3) + 2*a(n-4) - a(n-6) + a(n-7).

MATHEMATICA

CoefficientList[Series[(1+x^3+x^6)/(1-2x+x^3-2x^4+x^6-x^7), {x, 0, 40}], x] (* or *) LinearRecurrence[{2, 0, -1, 2, 0, -1, 1}, {1, 2, 4, 8, 16, 32, 64}, 40] (* Harvey P. Dale, Aug 10 2021 *)

CROSSREFS

Cf. A007931, A062257, A062259.

Sequence in context: A062257 A208127 A172316 * A239560 A066178 A122189

Adjacent sequences: A062255 A062256 A062257 * A062259 A062260 A062261

KEYWORD

nonn

AUTHOR

Vladeta Jovovic, Jun 14 2001

STATUS

approved

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Last modified January 26 16:14 EST 2023. Contains 359833 sequences. (Running on oeis4.)