OFFSET
1,1
REFERENCES
J.-M. Monier, Algèbre et géometrie, exercices corrigés. Dunod, 1997, p. 27.
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..80
FORMULA
a(1) = 2, a(n) = (1-n^(2*n+2))/(1-n^2) for n > 1.
EXAMPLE
a(5) = determinant(M_5) = 10172526 where M_5 is the matrix
[26 5 0 0 0]
[ 5 26 5 0 0]
[ 0 5 26 5 0]
[ 0 0 5 26 5]
[ 0 0 0 5 26]
MAPLE
with(numtheory):for n from 2 to 25 do:x:=(1-n^(2*n+2))/(1-n^2):print(x):od:
MATHEMATICA
M[j_, k_, n_]:=If[j==k, n^2+1, If[Abs[j-k]==1, n, 0]]; a[n_]:=Det[Table[M[j, k, n], {j, n}, {k, n}]]; Array[a, 13] (* Stefano Spezia, Aug 01 2026 *)
PROG
(Magma) [ n eq 1 select 2 else (1-n^(2*n+2))/(1-n^2): n in [1..13] ]; // Klaus Brockhaus, Apr 15 2010
(Magma) [ Determinant( SymmetricMatrix( &cat[ [k eq j select n^2+1 else k eq j-1 select n else 0: k in [1..j] ]: j in [1..n] ] ) ): n in [1..13] ]; // Klaus Brockhaus, Apr 15 2010
CROSSREFS
KEYWORD
nonn
AUTHOR
Michel Lagneau, Apr 02 2010
EXTENSIONS
Edited by Klaus Brockhaus, Apr 15 2010
STATUS
approved
