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This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A334251 a(n) is the number of binary (0,1) sequences of length n that have at most two zeros in a window of seven consecutive symbols.

Original entry on oeis.org

1, 2, 4, 7, 11, 16, 22, 29, 43, 66, 102, 157, 239, 358, 526, 777, 1159, 1740, 2619, 3942, 5923, 8870, 13259, 19822, 29667, 44451, 66641, 99912, 149745, 224338, 335993, 503199, 753720, 1129164, 1691796, 2534807, 3797721, 5689507, 8523275, 12768309, 19127928, 28655867, 42930562
Offset: 0

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Author

Kees Immink, Apr 20 2020

Keywords

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. We investigate binary systems emitting 0's and 1's signals where it is assumed that the 1's carry the energy. 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, t

Examples

			a(3) = 7 as there are 8 possible binary (0,1) sequences of length 3 but exactly one of them has more than 2 zero's in a window of seven consecutive symbols (the sequence (000)) leaving 8-1 = 7 such sequences. - _David A. Corneth_, Apr 20 2020

Links

Crossrefs

Cf. A118647, A120118, A133523.

Formula

G.f.: (x^20 +x^19 +x^18 +2*x^17 +2*x^16 +x^15 -3*x^13 -4*x^12 -5*x^11 -7*x^10 -5*x^9 -3*x^8 -3*x^7 +2*x^6 +3*x^5 +3*x^4 +3*x^3 +2*x^2 +x +1) / (-x^21 -x^18 +x^15 +3*x^14 +x^12 +2*x^11 -3*x^7 -x^4 -x +1).
From David A. Corneth, Apr 21 2020: (Start)
a(n) ~ c*r^n where c = 1.81880731105 and r = 1.498122533939865577.
a(n) = a(n - 1) + a(n - 4) + 3*a(n - 6) - 2*a(n - 10) - a(n - 12) - 3*a(n - 13) - a(n - 15) + a(n - 18) + a(n - 21), n >= 21. (End)

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