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 A109649 #12 Jan 20 2025 09:02:20 %S A109649 1,1,1,1,2,1,2,2,1,1,3,3,1,3,6,3,3,3,1,1,4,6,4,1,4,12,12,4,6,12,6,4,4, %T A109649 1,1,5,10,10,5,1,5,20,30,20,5,10,30,30,10,10,20,10,5,5,1,1,6,15,20,15, %U A109649 6,1,6,30,60,60,30,6,15,60,90,60,15,20,60,60,20,15,30,15,6 %N A109649 Entries in 3-dimensional version of Pascal triangle: trinomial coefficients. %C A109649 Greatest numbers in each 2D triangle form A022916 (multinomial coefficient n!/([n/3]![(n+1)/3]![(n+2)/3]!)). %C A109649 2D triangle sums are powers of 3. %C A109649 See A046816 for another version. %F A109649 Coefficients of x, y, z in (x+y+z)^n. %e A109649 .1 3 3 1 ... Here is the third slice of the pyramid %e A109649 . 3 6 3 %e A109649 .. 3 3 %e A109649 ... 1 ..... %Y A109649 Cf. A022916, A046816. %Y A109649 Cf. A007318, A002378, A027480, A033487, A033488. %K A109649 nonn,tabf,easy %O A109649 0,5 %A A109649 _Philippe Deléham_, Aug 03 2005