|
|
A078126
|
|
Negative determinant of n X n matrix M_{i,j}=1 if i=j or i+j=1 (mod 2).
|
|
3
|
|
|
-1, -1, 0, 1, 3, 5, 8, 11, 15, 19, 24, 29, 35, 41, 48, 55, 63, 71, 80, 89, 99, 109, 120, 131, 143, 155, 168, 181, 195, 209, 224, 239, 255, 271, 288, 305, 323, 341, 360, 379, 399, 419, 440, 461, 483, 505, 528, 551, 575, 599, 624, 649, 675, 701, 728, 755, 783, 811
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,5
|
|
COMMENTS
|
Apparently, also 6(n+3) times the Dedekind sum s(2,n+3). - Ralf Stephan, Sep 16 2013
|
|
LINKS
|
|
|
FORMULA
|
G.f.: (-1 + x + 2*x^2 - x^3) / ((1 - x^2) * (1 - x)^2).
a(n) = A024206(n-1) for all n in Z.
|
|
EXAMPLE
|
G.f. = -1 - x + x^3 + 3*x^4 + 5*x^5 + 8*x^6 + 11*x^7 + 15*x^8 + 19*x^9 + ...
|
|
MAPLE
|
|
|
MATHEMATICA
|
LinearRecurrence[{2, 0, -2, 1}, {-1, -1, 0, 1}, 60] (* Harvey P. Dale, Sep 10 2015 *)
|
|
PROG
|
(PARI) a(n)=-matdet(matrix(n, n, i, j, i==j||((i+j)%2))) /* Ralf Stephan, Sep 16 2013 */
(PARI) a(n)=sumdedekind(2, n+3)*6*(n+3) /* Ralf Stephan, Sep 16 2013 */
|
|
CROSSREFS
|
|
|
KEYWORD
|
sign,easy,nice
|
|
AUTHOR
|
|
|
EXTENSIONS
|
A-number twister corrected in cross-refs by R. J. Mathar, Feb 11 2010
|
|
STATUS
|
approved
|
|
|
|