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 A187081 #23 Mar 11 2022 07:45:57 %S A187081 1,0,1,0,1,0,0,1,0,0,0,1,1,0,0,0,1,2,0,0,0,0,1,4,0,0,0,0,0,1,7,0,0,0, %T A187081 0,0,0,1,12,0,0,0,0,0,0,0,1,20,1,0,0,0,0,0,0,0,1,33,2,0,0,0,0,0,0,0,0, %U A187081 1,54,5,0,0,0,0,0,0,0,0,0,1,88,11,0,0,0,0,0,0,0,0,0,0,1,143,22,0,0,0,0,0,0,0,0,0,0,0,1,232,44,0,0,0,0,0,0,0,0,0,0,0,0,1,376,84,0,0 %N A187081 Triangle T(n,k) read by rows: sandpiles of n grains and height k. %C A187081 See A186085 for the definition of sandpiles. %F A187081 For n>=2 we have T(n,1)+T(n,2) = Fibonacci(n-1). %F A187081 T(n,2) = A000071(n). [_Joerg Arndt_, Sep 17 2013] %e A187081 Triangle begins: %e A187081 1; %e A187081 0,1; %e A187081 0,1,0; %e A187081 0,1,0,0; %e A187081 0,1,1,0,0; %e A187081 0,1,2,0,0,0; %e A187081 0,1,4,0,0,0,0; %e A187081 0,1,7,0,0,0,0,0; %e A187081 0,1,12,0,0,0,0,0,0; %e A187081 0,1,20,1,0,0,0,0,0,0; %e A187081 0,1,33,2,0,0,0,0,0,0,0; %e A187081 0,1,54,5,0,0,0,0,0,0,0,0; %e A187081 0,1,88,11,0,0,0,0,0,0,0,0,0; %e A187081 0,1,143,22,0,0,0,0,0,0,0,0,0,0; %e A187081 0,1,232,44,0,0,0,0,0,0,0,0,0,0,0; %e A187081 0,1,376,84,0,0,0,0,0,0,0,0,0,0,0,0; %e A187081 0,1,609,158,1,0,0,0,0,0,0,0,0,0,0,0,0; %e A187081 0,1,986,293,2,0,0,0,0,0,0,0,0,0,0,0,0,0; %e A187081 0,1,1596,535,5,0,0,0,0,0,0,0,0,0,0,0,0,0,0; %e A187081 0,1,2583,969,12,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0; %e A187081 0,1,4180,1739,25,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0; %e A187081 0,1,6764,3099,52,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0; %e A187081 0,1,10945,5491,103,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0; %e A187081 The 22 compositions corresponding to sandpiles of 9 grains are the following: %e A187081 #: composition height %e A187081 1: [ 1 2 3 2 1 ] 3 %e A187081 2: [ 1 2 2 2 1 1 ] 2 %e A187081 3: [ 1 2 2 1 2 1 ] 2 %e A187081 4: [ 1 2 1 2 2 1 ] 2 %e A187081 5: [ 1 1 2 2 2 1 ] 2 %e A187081 6: [ 1 2 2 1 1 1 1 ] 2 %e A187081 7: [ 1 2 1 2 1 1 1 ] 2 %e A187081 8: [ 1 1 2 2 1 1 1 ] 2 %e A187081 9: [ 1 2 1 1 2 1 1 ] 2 %e A187081 10: [ 1 1 2 1 2 1 1 ] 2 %e A187081 11: [ 1 1 1 2 2 1 1 ] 2 %e A187081 12: [ 1 2 1 1 1 2 1 ] 2 %e A187081 13: [ 1 1 2 1 1 2 1 ] 2 %e A187081 14: [ 1 1 1 2 1 2 1 ] 2 %e A187081 15: [ 1 1 1 1 2 2 1 ] 2 %e A187081 16: [ 1 2 1 1 1 1 1 1 ] 2 %e A187081 17: [ 1 1 2 1 1 1 1 1 ] 2 %e A187081 18: [ 1 1 1 2 1 1 1 1 ] 2 %e A187081 19: [ 1 1 1 1 2 1 1 1 ] 2 %e A187081 20: [ 1 1 1 1 1 2 1 1 ] 2 %e A187081 21: [ 1 1 1 1 1 1 2 1 ] 2 %e A187081 22: [ 1 1 1 1 1 1 1 1 1 ] 1 %e A187081 stats: 0 1 20 1 0 0 0 0 0 0 %Y A187081 Row sums are A186085 (sandpiles of n grains), cf. A186084 (sandpiles by base length), A047998 (fountains of coins by base length). %K A187081 nonn,tabl %O A187081 0,18 %A A187081 _Joerg Arndt_, Mar 08 2011