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A363376 Determinant of the n X n matrix formed by placing 1..n^2 in L-shaped gnomons in alternating directions. 2
1, -5, 78, -1200, 19680, -351360, 6854400, -145797120, 3367526400, -84072038400, 2258332876800, -64990937088000, 1995834890649600, -65167516237824000, 2254974602969088000, -82443156980760576000, 3176032637949050880000, -128603097714237898752000, 5460911310769351557120000 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
The matrix is the upper-left n X n part of the square arrangement in A081344.
Number i is in the matrix at row A220604(i) column A220603(i), for i = 1..n^2.
Conjecture: a(n) has trailing zeros for n > 3. - Stefano Spezia, May 31 2023
LINKS
FORMULA
a(1) = 1, for a > 1: a(n) = (-1)^(n-1)*2^(n-3)*(2*n*(n-1)+1)*(n!). - Detlef Meya, Jun 11 2023
EXAMPLE
| 1----2 9---10 25 |
| | | | | |
| 4----3 8 11 24 |
| | | | | |
a(5) = | 5----6----7 12 23 | = 19680.
| | | |
| 16---15---14---13 22 |
| | | |
| 17---18---19---20---21 |
MATHEMATICA
a={}; For[n=1, n<=19, n++, k=i=j=1; M[i, j]=k++; For[h=1, h<n, h++, If[i==j==1, M[i, ++j]=k++; For[c=1, c<=h, c++, M[++i, j]=k++; M[i, --j]=k++], If[j==1 && i!=1, M[++i, j]=k++; For[c=1, c<=h, c++, M[i, ++j]=k++]; For[c=1, c<=h, c++, M[--i, j]=k++], If[i==1 &&j!=1, M[i, ++j]=k++; For[c=1, c<=h, c++, M[++i, j]=k++]; For[c=1, c<=h, c++, M[i, --j]=k++]]]]]; AppendTo[a, Det[Table[M[i, j], {i, n}, {j, n}]]]]; a (* Stefano Spezia, May 31 2023 *)
a={1}; For[n=2, n<20, n++, AppendTo[a, (-1)^(n-1)*2^(n-3)*(2*n*(n-1)+1)*n!]]; a (* Detlef Meya, Jun 11 2023 *)
CROSSREFS
Sequence in context: A327903 A214443 A015973 * A136578 A057186 A106939
KEYWORD
sign
AUTHOR
Nicolay Avilov, May 29 2023
EXTENSIONS
a(16)-a(19) from Stefano Spezia, May 31 2023
STATUS
approved

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Last modified April 23 03:30 EDT 2024. Contains 371906 sequences. (Running on oeis4.)