The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A335247 a(n) is the number of binary (0,1) sequences of length n that have at least two ones in each window of eight consecutive symbols. 2
 1, 2, 4, 8, 16, 32, 64, 127, 247, 487, 961, 1897, 3745, 7393, 14593, 28801, 56833, 112156, 221341, 436825, 862094, 1701380, 3357739, 6626611, 13077820, 25809478, 50935832, 100523529, 198386490, 391522260, 772682018, 1524913233, 3009466064, 5939279536, 11721362180 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Application: Not all electronic devices connected to the Internet of Things (IoT) have batteries or are connected to the power cable. These self-contained devices must rely on the harvesting of energy of the signals sent by a transmitter. A minimal number of 1's in transmitted sequences is required so as to carry sufficient energy within a prescribed time span. A binary sequence is said to obey the sliding-window (ell,t)-constraint if the number of 1's within any window of ell consecutive bits of that sequence is at least t, t28. a(n) ~ c*r^n where c = 1.07317641333 and r = 1.9735326811117101072. MATHEMATICA CoefficientList[Series[-(x^27 +x^26 -x^23 -x^22 -3*x^19 -5*x^18 -3*x^17 +3*x^15 +4*x^14 +2*x^13 +3*x^11 +5*x^10 +5*x^9 +3*x^8 -3*x^7 -3*x^6 -2*x^5 -x^4 -x^3 -x^2 -x -1) / (x^28 -x^24 -3*x^20 -3*x^19 +3*x^16 +2*x^15 +3*x^12 +4*x^11 +3*x^10 -3*x^8 -2*x^7 -x^6 -x^4 -x^3 -x^2 -x +1), {x, 0, 100}], x] (* Georg Fischer, Oct 26 2020 *) LinearRecurrence[{1, 1, 1, 1, 0, 1, 2, 3, 0, -3, -4, -3, 0, 0, -2, -3, 0, 0, 3, 3, 0, 0, 0, 1, 0, 0, 0, -1}, {1, 2, 4, 8, 16, 32, 64, 127, 247, 487, 961, 1897, 3745, 7393, 14593, 28801, 56833, 112156, 221341, 436825, 862094, 1701380, 3357739, 6626611, 13077820, 25809478, 50935832, 100523529}, 40] (* Harvey P. Dale, Feb 21 2022 *) CROSSREFS Cf. A118647, A120118, A133523, A334251, A133551. Sequence in context: A054044 A325741 A008859 * A145113 A062257 A208127 Adjacent sequences: A335244 A335245 A335246 * A335248 A335249 A335250 KEYWORD nonn,easy AUTHOR Kees Immink, May 28 2020 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified June 25 12:23 EDT 2024. Contains 373701 sequences. (Running on oeis4.)