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 A369892 #35 Feb 05 2025 09:20:25 %S A369892 1,3,1,7,7,1,15,37,17,1,31,175,197,41,1,63,781,1985,1041,99,1,127, %T A369892 3367,18621,22193,5503,239,1,255,14197,167337,433801,247759,29089,577, %U A369892 1,511,58975,1461797,8057625,10056087,2764991,153769,1393,1,1023,242461,12519345,144762849,384409519,232777209,30856705,812849,3363,1 %N A369892 Array read by antidiagonals: T(m, n) is the number of m X n binary arrays with a path of adjacent 1's from top row to bottom row using only left, right, and downward steps. %C A369892 Similar to A359576 but disallowing Up steps. %C A369892 The sequences are initially similar but differ for 4 X 5 grids (433801 instead of 433809), 4 X 6 grids (8057625 instead of 8057905), and 5 X 5 grids (10056087 instead of 10056959) %C A369892 Can be calculated by dynamic programming from 1 X n grids to m X n grids by keeping track of the number of grids with each of the 2^n patterns of reachable squares in the last row. %C A369892 Each row and each column satisfies a linear recurrence with constant coefficients. - _Pontus von Brömssen_, Feb 05 2025 %H A369892 Caleb Stanford, <a href="https://github.com/cdstanford/curiosities/tree/master/fish-friendly">Rust program to compute the sequence</a>. %e A369892 For the 37 2 X 3 grids, see A359576. %e A369892 The following 4 X 5 grid is a counterexample that is counted by A359576 but not by the present sequence: %e A369892 10000 %e A369892 10111 %e A369892 11101 %e A369892 00001 %e A369892 Notice that there is a path of 1s from the top to the bottom, but only via the upward step detour in the third column. There are 8 such 4 X 5 grids, formed from the above by reflection and by toggling the first row, second column and last row, second to last column. %e A369892 Table starts: %e A369892 1 3 7 15 31 63 127 ... %e A369892 1 7 37 175 781 3367 14197 ... %e A369892 1 17 197 1985 18621 167337 1461797 ... %e A369892 1 41 1041 22193 433801 8057625 144762849 ... %e A369892 1 99 5503 247759 10056087 384409519 ... %e A369892 1 239 29089 2764991 232777209 ... %e A369892 1 577 153769 30856705 ... %e A369892 1 1393 812849 ... %e A369892 1 3363 ... %e A369892 1 ... %e A369892 ... %Y A369892 First 4 rows are A000225, A005061, A069361, A368809. %Y A369892 First 4 columns are A000012, A001333, A069378, A069379. %Y A369892 Cf. A359576 (up steps allowed). %K A369892 nonn,tabl %O A369892 1,2 %A A369892 _Caleb Stanford_, Feb 05 2024