cp's OEIS Frontend

A361292 Square array A(n, k), n, k >= 0, read by antidiagonals; A(0, 0) = 1, and otherwise A(n, k) is the sum of all terms in previous antidiagonals at one knight's move away.

%I A361292 #20 Oct 17 2023 10:55:39
%S A361292 1,0,0,0,0,0,0,1,1,0,1,1,0,1,1,1,0,2,2,0,1,0,2,4,2,4,2,0,2,5,4,7,7,4,
%T A361292 5,2,5,5,10,14,12,14,10,5,5,5,10,21,23,30,30,23,21,10,5,10,23,35,49,
%U A361292 62,60,62,49,35,23,10,23,40,69,100,119,137,137,119,100,69,40,23
%N A361292 Square array A(n, k), n, k >= 0, read by antidiagonals; A(0, 0) = 1, and otherwise A(n, k) is the sum of all terms in previous antidiagonals at one knight's move away.
%H A361292 Paolo Xausa, <a href="/A361292/b361292.txt">Table of n, a(n) for n = 0..11324</a> (antidiagonals 1..150 of the array, flattened).
%H A361292 Rémy Sigrist, <a href="/A361292/a361292.gp.txt">PARI program</a>
%F A361292 A(n, k) = A(k, n).
%F A361292 A(n, k) = A'(n-2, k-1) + A'(n-2, k+1) + A'(n-1, k-2) + A'(n+1, k-2) for n + k > 0 (where A' extends A with 0's outside its domain of definition).
%e A361292 Square array A(n, k) begins:
%e A361292   n\k |  0   1    2    3     4     5     6      7      8      9      10
%e A361292   ----+----------------------------------------------------------------
%e A361292     0 |  1   0    0    0     1     1     0      2      5      5      10
%e A361292     1 |  0   0    1    1     0     2     5      5     10     23      40
%e A361292     2 |  0   1    0    2     4     4    10     21     35     69     138
%e A361292     3 |  0   1    2    2     7    14    23     49    100    190     382
%e A361292     4 |  1   0    4    7    12    30    62    119    250    512    1031
%e A361292     5 |  1   2    4   14    30    60   137    290    599   1263    2639
%e A361292     6 |  0   5   10   23    62   137   298    662   1430   3043    6502
%e A361292     7 |  2   5   21   49   119   290   662   1472   3281   7181   15569
%e A361292     8 |  5  10   35  100   250   599  1430   3281   7410  16585   36699
%e A361292     9 |  5  23   69  190   512  1263  3043   7181  16585  37700   84939
%e A361292    10 | 10  40  138  382  1031  2639  6502  15569  36699  84939  194154
%t A361292 A361292list[dmax_]:=Module[{A},A[0,0]=1;A[n_,k_]:=A[n,k]=A[k,n]=If[n>=0&&k>=0,A[n-2,k-1]+A[n-2,k+1]+A[n-1,k-2]+A[n+1,k-2],0];Table[A[n-k,k],{n,0,dmax-1},{k,0,n}]];A361292list[15] (* Generates 15 antidiagonals *) (* _Paolo Xausa_, Oct 17 2023 *)
%o A361292 (PARI) See Links section.
%Y A361292 See A355320 for a similar sequence.
%K A361292 nonn,tabl
%O A361292 0,18
%A A361292 _Rémy Sigrist_, Mar 12 2023