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.
%I A095142 #34 Apr 30 2025 15:04:46
%S A095142 1,1,1,1,2,1,1,3,3,1,1,4,6,4,1,1,5,3,3,5,1,1,6,1,6,1,6,1,1,0,0,0,0,0,
%T A095142 0,1,1,1,0,0,0,0,0,1,1,1,2,1,0,0,0,0,1,2,1,1,3,3,1,0,0,0,1,3,3,1,1,4,
%U A095142 6,4,1,0,0,1,4,6,4,1,1,5,3,3,5,1,0,1,5,3,3,5,1,1,6,1,6,1,6,1,1,6,1,6,1,6,1
%N A095142 Triangle, read by rows, formed by reading Pascal's triangle (A007318) mod 7.
%C A095142 {T(n,k)} is a fractal gasket with fractal (Hausdorff) dimension log(A000217(7))/log(7) = log(28)/log(7) = 1.71241... (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
%D A095142 Boris A. Bondarenko, Generalized Pascal Triangles and Pyramids (in Russian), FAN, Tashkent, 1990, ISBN 5-648-00738-8.
%D A095142 Michel Rigo, Formal Languages, Automata and Numeration Systems, 2 vols., Wiley, 2014. Mentions this sequence - see "List of Sequences" in Vol. 2.
%H A095142 Ilya Gutkovskiy, <a href="/A275198/a275198.pdf">Illustrations (triangle formed by reading Pascal's triangle mod m)</a>
%H A095142 Boris A. Bondarenko, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/pascal.html">Generalized Pascal Triangles and Pyramids</a>, English translation published by Fibonacci Association, Santa Clara Univ., Santa Clara, CA, 1993; see pp. 130-132.
%H A095142 A. M. Reiter, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Issues/31-2.pdf">Determining the dimension of fractals generated by Pascal's triangle</a>, Fibonacci Quarterly, 31(2), 1993, pp. 112-120.
%H A095142 <a href="/index/Pas#Pascal">Index entries for triangles and arrays related to Pascal's triangle</a>
%F A095142 T(i, j) = binomial(i, j) mod 7.
%t A095142 Mod[ Flatten[ Table[ Binomial[n, k], {n, 0, 13}, {k, 0, n}]], 7]
%o A095142 (Python)
%o A095142 from math import comb, isqrt
%o A095142 def A095142(n):
%o A095142 def f(m,k):
%o A095142 if m<7 and k<7: return comb(m,k)%7
%o A095142 c,a = divmod(m,7)
%o A095142 d,b = divmod(k,7)
%o A095142 return f(c,d)*f(a,b)%7
%o A095142 return f(r:=(m:=isqrt(k:=n+1<<1))-(k<=m*(m+1)),n-comb(r+1,2)) # _Chai Wah Wu_, Apr 30 2025
%Y A095142 Cf. A007318, A047999, A083093, A034931, A095140, A095141, A034930, A095143, A008975, A095144, A095145, A034932.
%Y A095142 Sequences based on the triangles formed by reading Pascal's triangle mod m: A047999 (m = 2), A083093 (m = 3), A034931 (m = 4), A095140 (m = 5), A095141 (m = 6), (this sequence) (m = 7), A034930(m = 8), A095143 (m = 9), A008975 (m = 10), A095144 (m = 11), A095145 (m = 12), A275198 (m = 14), A034932 (m = 16).
%K A095142 easy,nonn,tabl
%O A095142 0,5
%A A095142 _Robert G. Wilson v_, May 29 2004