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 A206427 #30 Dec 18 2020 04:07:18 %S A206427 1,2,2,5,4,4,14,10,8,8,41,28,20,16,16,122,82,56,40,32,32,365,244,164, %T A206427 112,80,64,64,1094,730,488,328,224,160,128,128,3281,2188,1460,976,656, %U A206427 448,320,256,256,9842,6562,4376,2920,1952,1312,896,640,512,512 %N A206427 Square array 2^(m-1)*(3^n+1), read by antidiagonals. %C A206427 Rectangular array giving the number of 1's in any row of Pascal's Triangle (mod 3) whose row number has exactly m 1's and n 2's in its ternary expansion (listed by antidiagonals). %C A206427 a(m,n) is independent of the number of zeros in the ternary expansion of the row number. %C A206427 a(m,n) gives a non-recursive formula for A206424. %H A206427 Marcus Jaiclin, et al. <a href="https://web.archive.org/web/20170823000349/http://pyrrho.wsc.ma.edu/math/faculty/jaiclin/writings/research/pascals_triangle/">Pascal's Triangle, Mod 2,3,5</a> %F A206427 a(m, n) = 2^(m - 1)(3^n + 1). %e A206427 Initial 5 X 5 block of entries (upper corner is (m,n)=(0,0), m increases down, n increases across): %e A206427 1 2 5 14 41 %e A206427 2 4 10 28 82 %e A206427 4 8 20 56 164 %e A206427 8 16 40 112 328 %e A206427 16 32 80 224 656 %e A206427 Pascal's Triangle (mod 3), row numbers in ternary: %e A206427 1 <= Row 0, m = 0, n = 0, 2^(-1)(3^0 + 1) = #1's = 1 %e A206427 1 1 <= Row 1, m = 1, n = 0, 2^0(3^0 + 1) = #1's = 2 %e A206427 1 2 1 <= Row 2, m = 0, n = 1, 2^(-1)(3^1 + 1) = #1's = 2 %e A206427 1 0 0 1 <= Row 10, m = 1, n = 0, 2^0(3^0 + 1) = #1's = 2 %e A206427 1 1 0 1 1 <= Row 11, m = 2, n = 0, 2^1(3^0 + 1) = #1's = 4 %e A206427 1 2 1 1 2 1 <= Row 12, m = 1, n = 1, 2^0(3^1 + 1) = #1's = 4 %e A206427 1 0 0 2 0 0 1 <= Row 20, m = 0, n = 1, 2^(-1)(3^1 + 1) = #1's = 2 %e A206427 1 1 0 2 2 0 1 1 <= Row 21, m = 1, n = 1, 2^0(3^1 + 1) = #1's = 4 %e A206427 1 2 1 2 1 2 1 2 1 <= Row 22, m = 0, n = 2, 2^(-1)(3^2 + 1) = #1's = 5 %e A206427 1 0 0 0 0 0 0 0 0 1 <= Row 100, m = 1, n = 0, 2^0(3^0 + 1) = #1's = 2 %Y A206427 Cf. A206428, A206424, A227428, A083093, A077267, A062756, A081603. %Y A206427 Cf. A062296, A006047, A007318. %K A206427 nonn,tabl %O A206427 0,2 %A A206427 _Marcus Jaiclin_, Feb 07 2012