login
A174964
Determinant of the symmetric n X n matrix M_n where M_n(j,k) = n^2+1 for j = k, M_n(j,k) = n for abs(j-k) = 1, M_n(j,k) = 0 otherwise.
2
2, 21, 820, 69905, 10172526, 2238976117, 692352720200, 285942833483841, 151970818238211610, 101010101010101010101, 82081105631730092455932, 80052769211806164721787281, 92279361920609501281366280390
OFFSET
1,1
REFERENCES
J.-M. Monier, Algèbre et géometrie, exercices corrigés. Dunod, 1997, p. 27.
LINKS
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:
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
Cf. A174963.
Sequence in context: A342267 A376689 A113083 * A210830 A139164 A019994
KEYWORD
nonn
AUTHOR
Michel Lagneau, Apr 02 2010
EXTENSIONS
Edited by Klaus Brockhaus, Apr 15 2010
STATUS
approved