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, 21, 820, 69905, 10172526, 2238976117, 692352720200, 285942833483841, 151970818238211610, 101010101010101010101, 82081105631730092455932, 80052769211806164721787281, 92279361920609501281366280390
Offset: 1
Keywords
Examples
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]
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
Crossrefs
Cf. A174963.
Programs
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Magma
[ n eq 1 select 2 else (1-n^(2*n+2))/(1-n^2): n in [1..13] ]; // Klaus Brockhaus, Apr 15 2010
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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
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Maple
with(numtheory):for n from 2 to 25 do:x:=(1-n^(2*n+2))/(1-n^2):print(x):od:
Formula
a(1) = 2, a(n) = (1-n^(2*n+2))/(1-n^2) for n > 1.
Extensions
Edited by Klaus Brockhaus, Apr 15 2010