A095140 Triangle, read by rows, formed by reading Pascal's triangle (A007318) mod 5.

1, 1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 4, 1, 4, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 2, 1, 0, 0, 1, 2, 1, 1, 3, 3, 1, 0, 1, 3, 3, 1, 1, 4, 1, 4, 1, 1, 4, 1, 4, 1, 1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 2, 2, 0, 0, 0, 1, 1, 1, 2, 1, 0, 0, 2, 4, 2, 0, 0, 1, 2, 1, 1, 3, 3, 1, 0, 2, 1, 1, 2, 0, 1, 3, 3, 1

Offset

0,5

Comments

{T(n,k)} is a fractal gasket with fractal (Hausdorff) dimension log(A000217(5))/log(5) = log(15)/log(5) = 1.68260... (see Reiter reference). Replacing values greater than 1 with 1 produces a binary gasket with the same dimension (see Bondarenko reference). - Richard L. Ollerton, Dec 14 2021

References

B. A. Bondarenko, Generalized Pascal Triangles and Pyramids, Santa Clara, Calif.: The Fibonacci Association, 1993, pp. 130-132.

Links

Table of n, a(n) for n=0..104.

Ilya Gutkovskiy, Illustrations (triangle formed by reading Pascal's triangle mod m)

A. M. Reiter, Determining the dimension of fractals generated by Pascal's triangle, Fibonacci Quarterly, 31(2), 1993, pp. 112-120.

Index entries for triangles and arrays related to Pascal's triangle

Formula

T(i, j) = binomial(i, j) mod 5.

Mathematica

Mod[ Flatten[ Table[ Binomial[n, k], {n, 0, 13}, {k, 0, n}]], 5]

Crossrefs

Cf. A007318, A047999, A083093, A034931, A095141, A095142, A034930, A095143, A008975, A095144, A095145, A034932.

Sequences based on the triangles formed by reading Pascal's triangle mod m: A047999 (m = 2), A083093 (m = 3), A034931 (m = 4), (this sequence) (m = 5), A095141 (m = 6), A095142 (m = 7), A034930(m = 8), A095143 (m = 9), A008975 (m = 10), A095144 (m = 11), A095145 (m = 12), A275198 (m = 14), A034932 (m = 16).

Sequence in context: A370399 A095141 A177974 * A225043 A125605 A110570

Adjacent sequences: A095137 A095138 A095139 * A095141 A095142 A095143

Keyword

easy,nonn,tabl

Author

Robert G. Wilson v, May 29 2004

Status

approved