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 A059036 #37 Feb 22 2022 09:58:01
%S A059036 0,1,1,2,3,2,3,5,5,3,4,7,8,7,4,5,9,11,11,9,5,6,11,14,15,14,11,6,7,13,
%T A059036 17,19,19,17,13,7,8,15,20,23,24,23,20,15,8,9,17,23,27,29,29,27,23,17,
%U A059036 9,10,19,26,31,34,35,34,31,26,19,10,11,21,29,35,39,41
%N A059036 In a triangle of numbers (such as that in A059032, A059033, A059034) how many entries lie above position (n,k)? Answer: T(n,k) = (n+1)*(k+1)-1 (n >= 0, k >= 0).
%F A059036 T(n, k) = max(T(n-1, k-1), T(n-1, k)) + min(k, n-k+1). - _Jon Perry_, Aug 05 2004
%F A059036 E.g.f.: exp(x+y)(x+y+xy) (as a square array read by antidiagonals). - _Paul Barry_, Sep 24 2004
%F A059036 From _Michael Somos_, Jul 28 2015: (Start)
%F A059036 Row sums = Sum_{k=0..n} T(n-k, k) = A005581(n+1).
%F A059036 T(n, k) = T(k, n) = T(-2-n, -2-k) for all n, k in Z.
%F A059036 Sum_{n, k >= 0} x^T(n, k) = f(x) / x where f() is the g.f. for A000005. (End)
%e A059036 As an infinite triangular array:
%e A059036 0
%e A059036 1 1
%e A059036 2 3 2
%e A059036 3 5 5 3
%e A059036 4 7 8 7 4
%e A059036 5 9 11 11 9 5
%e A059036 As an infinite square array (matrix):
%e A059036 0 1 2 3 4 5
%e A059036 1 3 5 7 9 11
%e A059036 2 5 8 11 14 17
%e A059036 3 7 11 15 19 23
%e A059036 4 9 14 19 24 29
%e A059036 5 11 17 23 29 35
%o A059036 (PARI) {T(n, k) = n + k + n*k}; /* _Michael Somos_, Jul 28 2015 */
%Y A059036 T(n, k) = A003991(n, k) - 1.
%Y A059036 Cf. A000005, A005581.
%K A059036 nonn,tabl,easy
%O A059036 0,4
%A A059036 _N. J. A. Sloane_, Feb 13 2001