A062257
Number of (0,1)-strings of length n with no occurrences of the substrings 10101101 and 1110101.
Original entry on oeis.org
1, 2, 4, 8, 16, 32, 64, 127, 251, 496, 981, 1940, 3837, 7590, 15015, 29704, 58763, 116249, 229971, 454942, 899991, 1780410, 3522102, 6967611, 13783703, 27267665, 53942368, 106711708, 211102869, 417615105, 826148769, 1634332138
Offset: 0
- I. P. Goulden and D. M. Jackson, Combinatorial Enumeration, Wiley, N.Y., 1983, (Example 2.8.11).
A062258
Number of (0,1)-strings of length n not containing the substring 0100100.
Original entry on oeis.org
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
Offset: 0
- 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]
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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 *)
A140134
a(n)=2a(n-1) but when sum of digits of 2a(n-1) is greater than 9 take a(n) = largest number < 2a(n-1) which has sum of digits = 9.
Original entry on oeis.org
1, 2, 4, 8, 16, 32, 63, 126, 252, 504, 1008, 2016, 4032, 8001, 16002, 32004, 63000, 126000, 252000, 504000, 1008000, 2016000, 4032000, 8001000, 16002000, 32004000, 63000000, 126000000, 252000000, 504000000, 1008000000, 2016000000
Offset: 0
a(12)=4032; 2*4032 = 8064; digit sum is 18; decrease until we get a number with digit sum 9, which is 8001; so a(13) = 8001. - From _N. J. A. Sloane_, Oct 08 2012
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