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 A381703 #36 Mar 12 2025 07:55:06 %S A381703 1,1,1,1,1,1,3,1,2,3,6,1,1,6,5,7,15,1,2,11,5,7,39,25,18,1,1,10,19,7,3, %T A381703 59,96,35,77,61,1,3,22,28,7,1,42,210,188,49,181,383,97,73,1,1,15,52, %U A381703 40,9,21,255,550,332,63,266,1304,822,155,529,240,1,3,45,90,53,9,4,212,954,1231,529,81,251,2847,3548,1551,220,2413,2366,410,255 %N A381703 Irregular triangle read by rows in which every row of length A071764(n) lists A(n,w,h) = the number of free polyominoes of size n, width w and height h (for w <= h, and all possible w,h pairs). %H A381703 John Mason, <a href="/A381703/b381703.txt">Table of n, a(n) for n = 1..386</a> %e A381703 Triangle begins: %e A381703 n %e A381703 1: 1 %e A381703 2: 1 %e A381703 3: 1 1 %e A381703 4: 1 1 3 %e A381703 5: 1 2 3 6 %e A381703 6: 1 1 6 5 7 15 %e A381703 7: 1 2 11 5 7 39 25 18 %e A381703 8: 1 1 10 19 7 3 59 96 35 77 61 %e A381703 9: 1 3 22 28 7 1 42 210 188 49 181 383 97 73 %e A381703 10: 1 1 15 52 40 9 21 255 550 332 63 266 1304 822 155 529 240 %e A381703 ... %e A381703 Any row contains an irregular array that shows the number of polyominoes having width w and height h. E.g., row 6 contains the array: %e A381703 h/w 1 2 3 %e A381703 1 %e A381703 2 %e A381703 3 1 7 %e A381703 4 6 15 %e A381703 5 5 %e A381703 6 1 %e A381703 . %e A381703 There are 5 polyominoes of size 6 with width 2 and height 5, so A(6,2,5)=5: %e A381703 . %e A381703 OO O O O O %e A381703 O OO O O O %e A381703 O O OO O OO %e A381703 O O O OO O %e A381703 O O O O O %Y A381703 Row sums give A000105. %Y A381703 Row lengths give A071764. %Y A381703 Cf. A379623, A379624, A379625, A317186. %K A381703 nonn,hard,tabf %O A381703 1,7 %A A381703 _John Mason_, Mar 04 2025 %E A381703 More terms from _John Mason_, Mar 07 2025