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 A375763 #10 Aug 29 2024 02:10:47
%S A375763 1,1,1,1,1,2,2,2,1,1,1,3,4,5,4,4,3,2,1,1,1,4,7,10,11,11,11,9,8,6,5,3,
%T A375763 2,1,1,1,5,11,18,24,27,30,29,28,25,23,19,16,12,10,7,5,3,2,1,1,1,6,16,
%U A375763 30,46,59,71,78,81,81,78,74,67,60,52,46,37,31,24
%N A375763 Irregular triangle read by rows, T(n,k) is the number of North-East lattice paths from (0,0) to (n,n+2) that stay weakly above y = x, with weight = k + A000217(n).
%C A375763 Here the weight of a lattice path is the area under the path and above the x-axis. T(n,k) also counts the number of integer compositions of (3*n) + (2*k) + 6 with adjacent differences in {-1,1}, first part 1, and last part 3.
%H A375763 John Tyler Rascoe, <a href="/A375763/a375763_1.py.txt">Python program</a>.
%e A375763 Triangle begins:
%e A375763 k=0 1 2 3 4 5 6 7 8 9 10 11 12 13 14
%e A375763 n=0: 1;
%e A375763 n=1: 1, 1, 1;
%e A375763 n=2: 1, 2, 2, 2, 1, 1;
%e A375763 n=3: 1, 3, 4, 5, 4, 4, 3, 2, 1, 1;
%e A375763 n=4: 1, 4, 7, 10, 11, 11, 11, 9, 8, 6, 5, 3, 2, 1, 1;
%e A375763 ...
%e A375763 T(1,0) = 1: (NENN).
%e A375763 T(2,1) = 2: (NNEENN) and (NENNEN).
%e A375763 T(3,2) = 4: (NENENNNE), (NENNENEN), (NNEENNEN), and (NNENEENN).
%o A375763 (Python) # see linked program
%Y A375763 Cf. A000245 (empirical row sums), A000217 (row lengths).
%Y A375763 Cf. A227543 (paths of this kind from (0,0) to (n,n), offset 1 for (0,0) to (n,n+1)).
%Y A375763 Cf. A000108, A152659, A173258, A227543, A268429.
%K A375763 nonn,easy,tabf
%O A375763 0,6
%A A375763 _John Tyler Rascoe_, Aug 26 2024