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 A264071 #14 Mar 25 2025 21:55:20 %S A264071 2,5,4,13,21,8,34,121,89,16,89,605,1210,377,32,233,3025,12100,12100, %T A264071 1597,64,610,15125,131890,239580,121000,6765,128,1597,75625,1445345, %U A264071 5645376,4745620,1210000,28657,256,4181,378125,15892745,130697424,242621698,94000060,12100000,121393,512 %N A264071 T(n,k) = number of (n+1) X (k+1) arrays of permutations of 0..(n+1)*(k+1)-1 with each element having index change +-(.,.) 0,0 1,1 or 1,2. %H A264071 R. H. Hardin, <a href="/A264071/b264071.txt">Table of n, a(n) for n = 1..143</a> %F A264071 Empirical for column k: %F A264071 k=1: a(n) = 2*a(n-1) %F A264071 k=2: a(n) = 4*a(n-1) +a(n-2) %F A264071 k=3: a(n) = 10*a(n-1) for n>2 %F A264071 k=4: a(n) = 19*a(n-1) +16*a(n-2) for n>3 %F A264071 k=5: a(n) = 43*a(n-1) -43*a(n-3) +a(n-4) for n>5 %F A264071 k=6: a(n) = 87*a(n-1) +374*a(n-2) -470*a(n-3) +207*a(n-4) +3*a(n-5) for n>7 %F A264071 k=7: a(n) = 191*a(n-1) +1102*a(n-2) -7594*a(n-3) -38349*a(n-4) +38507*a(n-5) for n>8 %F A264071 Empirical for row n: %F A264071 n=1: a(n) = 3*a(n-1) -a(n-2) %F A264071 n=2: a(n) = 5*a(n-1) for n>3 %F A264071 n=3: a(n) = 12*a(n-1) -12*a(n-2) +12*a(n-3) -12*a(n-4) +a(n-5) for n>7 %F A264071 n=4: a(n) = 24*a(n-1) -19*a(n-2) -11*a(n-3) +36*a(n-4) +3*a(n-5) for n>9 %F A264071 n=5: [order 14] for n>19 %F A264071 n=6: [order 10] for n>19 %e A264071 Table starts: %e A264071 2 5 13 34 89 233 %e A264071 4 21 121 605 3025 15125 %e A264071 8 89 1210 12100 131890 1445345 %e A264071 16 377 12100 239580 5645376 130697424 %e A264071 32 1597 121000 4745620 242621698 11909009849 %e A264071 64 6765 1210000 94000060 10427064769 1084282319384 %e A264071 128 28657 12100000 1861931060 448121165789 98725402363225 %e A264071 256 121393 121000000 36880691100 19258783041289 8989061417123964 %e A264071 512 514229 1210000000 730524027860 827679549612058 818464496640651553 %e A264071 1024 2178309 12100000000 14470047586940 35570961850254336 74522143720797473932 %e A264071 ... %e A264071 Some solutions for n=3 k=4: %e A264071 ..0..8..9..3..4....6..1..2..3..4....7..8..2..3..4....0..8..2..3..4 %e A264071 ..5.13..7..1..2...11.13..0..8..9...12..6..0..1..9....5..6..7..1..9 %e A264071 .16.11.18..6.14...10..5.19..7.14...17..5.18.13.14...17.18.12.13.14 %e A264071 .15.10.17.12.19...15.16.17.18.12...15.16.10.11.19...15.16.10.11.19 %Y A264071 Main diagonal is A264066. %Y A264071 Columns 1,2 and 4..7 are A000079, A015448(n+1), A264067, A264068, A264069, A264070. %Y A264071 Rows 1 and 3..7 are A001519(n+1), A264072, A264073, A264074, A264075, A264076. %K A264071 nonn,tabl %O A264071 1,1 %A A264071 _R. H. Hardin_, Nov 02 2015 %E A264071 Name corrected by _Andrew Howroyd_, Mar 25 2025