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A283838 Irregular triangle read by rows: T(n,k) (n >= 8, 3 <= k <= floor(n/2)-1) = number of binary vectors of length <= n that start with 1^k, 0, end with 1, 0^k, and the factor between 1^k and 0^k does not contain 0^k or 1^k. 3
1, 3, 5, 1, 9, 3, 16, 7, 1, 26, 13, 3, 43, 25, 7, 1, 71, 47, 15, 3, 115, 88, 29, 7, 1, 187, 162, 57, 15, 3, 304, 299, 111, 31, 7, 1, 492, 551, 215, 61, 15, 3, 797, 1015, 416, 121, 31, 7, 1, 1291, 1867, 802, 239, 63, 15, 3, 2089, 3435, 1547, 471, 125, 31, 7, 1, 3381, 6319, 2983, 927, 249, 63, 15, 3 (list; graph; refs; listen; history; text; internal format)
OFFSET
8,2
LINKS
Stefano Bilotta, Variable-length Non-overlapping Codes, arXiv preprint arXiv:1605.03785 [cs.IT], 2016 [See Table 3].
EXAMPLE
Triangle begins:
1,
3,
5, 1,
9, 3,
16, 7, 1,
26, 13, 3,
43, 25, 7, 1,
71, 47, 15, 3,
115, 88, 29, 7, 1,
187, 162, 57, 15, 3,
304, 299, 111, 31, 7, 1,
492, 551, 215, 61, 15, 3,
797, 1015, 416, 121, 31, 7, 1,
1291, 1867, 802, 239, 63, 15, 3,
2089, 3435, 1547, 471, 125, 31, 7, 1,
3381, 6319, 2983, 927, 249, 63, 15, 3,
5472, 11624, 5751, 1824, 495, 127, 31, 7, 1,
...
MATHEMATICA
gf[k_] := x^(2k)(x-x^k)^2 / ((1-x)(1-x^k)(1-2x+x^k));
T[n_, k_] := SeriesCoefficient[gf[k], {x, 0, n}];
Table[T[n, k], {n, 8, 24}, {k, 3, Floor[n/2]-1}] // Flatten (* Jean-François Alcover, Apr 05 2017 *)
CROSSREFS
For row sums see A283839.
Sequence in context: A361944 A320386 A112411 * A228146 A328013 A241674
KEYWORD
nonn,tabf
AUTHOR
N. J. A. Sloane, Mar 25 2017
STATUS
approved

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Last modified July 12 16:21 EDT 2024. Contains 374251 sequences. (Running on oeis4.)