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%I #20 Oct 17 2023 10:55:39
%S 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 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 62,60,62,49,35,23,10,23,40,69,100,119,137,137,119,100,69,40,23
%N 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 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 Rémy Sigrist, <a href="/A361292/a361292.gp.txt">PARI program</a>
%F A(n, k) = A(k, n).
%F 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 Square array A(n, k) begins:
%e n\k | 0 1 2 3 4 5 6 7 8 9 10
%e ----+----------------------------------------------------------------
%e 0 | 1 0 0 0 1 1 0 2 5 5 10
%e 1 | 0 0 1 1 0 2 5 5 10 23 40
%e 2 | 0 1 0 2 4 4 10 21 35 69 138
%e 3 | 0 1 2 2 7 14 23 49 100 190 382
%e 4 | 1 0 4 7 12 30 62 119 250 512 1031
%e 5 | 1 2 4 14 30 60 137 290 599 1263 2639
%e 6 | 0 5 10 23 62 137 298 662 1430 3043 6502
%e 7 | 2 5 21 49 119 290 662 1472 3281 7181 15569
%e 8 | 5 10 35 100 250 599 1430 3281 7410 16585 36699
%e 9 | 5 23 69 190 512 1263 3043 7181 16585 37700 84939
%e 10 | 10 40 138 382 1031 2639 6502 15569 36699 84939 194154
%t 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 (PARI) See Links section.
%Y See A355320 for a similar sequence.
%K nonn,tabl
%O 0,18
%A _Rémy Sigrist_, Mar 12 2023