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 A181695 #13 Nov 04 2019 02:21:43
%S A181695 1,2,3,3,6,7,4,11,14,15,5,19,27,30,31,6,32,51,59,62,63,7,53,95,115,
%T A181695 123,126,127,8,87,176,223,243,251,254,255,9,142,325,431,479,499,507,
%U A181695 510,511,10,231,599,832,943,991,1011,1019,1022,1023,11,375,1103,1605
%N A181695 Triangle read by rows: T(n,m) = number of solutions x_1 + x_2 + ... + x_k <= n, where 1 <= x_i <= m, and any k >= 1.
%F A181695 For a fixed m, generating function is 1/(1-2*x+x^(m+1)) - 1/(1-x).
%F A181695 T(n,m) = Sum_{i=0..floor(n/(m+1))} binomial(n-mi, i)*(-1)^i*2^(n-(m+1)i) - 1.
%F A181695 T(n,m) = 2^m - 1 + Sum_{j=m+1..n} A126198(j,m).
%e A181695 Triangle begins:
%e A181695 1;
%e A181695 2, 3;
%e A181695 3, 6, 7;
%e A181695 4, 11, 14, 15;
%e A181695 5, 19, 27, 30, 31;
%e A181695 6, 32, 51, 59, 62, 63;
%e A181695 7, 53, 95, 115, 123, 126, 127;
%e A181695 ...
%e A181695 Could also be extended to a square array:
%e A181695 1, 1, 1, 1, 1, 1, 1, ...
%e A181695 2, 3, 3, 3, 3, 3, 3, ...
%e A181695 3, 6, 7, 7, 7, 7, 7, ...
%e A181695 4, 11, 14, 15, 15, 15, 15, ...
%e A181695 5, 19, 27, 30, 31, 31, 31, ...
%e A181695 6, 32, 51, 59, 62, 63, 63, ...
%e A181695 7, 53, 95, 115, 123, 126, 127, ...
%o A181695 (PARI) { T(n,m) = sum(i=0, n\(m+1), binomial(n-m*i,i) * (-1)^i * 2^(n-(m+1)*i) ) - 1 }
%Y A181695 Cf. A001911 (second column), A027084 (third column), A126198.
%K A181695 nonn,tabl
%O A181695 1,2
%A A181695 _Max Alekseyev_, Nov 17 2010