A283838 - OEIS

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.

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

Alois P. Heinz, Rows n = 8..290, flattened

Stefano Bilotta, Variable-length Non-overlapping Codes, arXiv preprint arXiv:1605.03785 [cs.IT], 2016 [See Table 3].

EXAMPLE

Triangle begins:

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

Cf. A094686, A283834-A283837.

For row sums see A283839.

Sequence in context: A361944 A320386 A112411 * A228146 A328013 A241674

Adjacent sequences: A283835 A283836 A283837 * A283839 A283840 A283841

KEYWORD

nonn,tabf

AUTHOR

N. J. A. Sloane, Mar 25 2017

STATUS

approved