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 A337131 #77 Mar 20 2025 14:42:27 %S A337131 1,1,1,1,2,1,1,1,1,4,2,1,2,1,1,1,1,2,1,4,8,2,2,1,1,4,2,1,2,1,1,1,1,2, %T A337131 1,2,4,1,1,4,4,16,8,2,4,2,2,1,1,2,1,4,8,2,2,1,1,4,2,1,2,1,1,1,1,2,1,2, %U A337131 4,1,1,2,2,8,4,1,2,1,1,4,4,8,4,16,32,8 %N A337131 Row lengths of irregular triangle A335967. %C A337131 All terms are powers of 2. %H A337131 Rémy Sigrist, <a href="/A337131/a337131.gp.txt">PARI program for A337131</a> %F A337131 a(2^k-1) = 1 for any k >= 0. %F A337131 a(2^k) = 1 for any k >= 0. %F A337131 a(A000975(k)) = 2^(k-2) for any k >= 2. %e A337131 For n = 13, the binary representation of 13 is "1101", so we consider the tilings of a size 4 staircase polyomino whose base has the following shape: %e A337131 ..... %e A337131 . . %e A337131 . ..... %e A337131 . . %e A337131 +---+ ..... %e A337131 | | . %e A337131 | +---+---+---+ %e A337131 | 1 1 | 0 | 1 | %e A337131 +-------+---+---+ %e A337131 There are two possible penultimate rows: %e A337131 ..... ..... %e A337131 . . . . %e A337131 . ..... . ..... %e A337131 . | . . . %e A337131 +---+ +---+ +---+---+---+ %e A337131 | 1 | 0 0 | | 1 | 0 | 1 | %e A337131 | +---+---+---+ | +---+---+---+ %e A337131 | | | | | | | | %e A337131 +-------+---+---+, +-------+---+---+ %e A337131 so a(13) = 2. %o A337131 (PARI) \\ See Links section. %Y A337131 Cf. A000975, A335967. %K A337131 nonn %O A337131 1,5 %A A337131 _Rémy Sigrist_, Sep 14 2020