|
| |
|
|
A030640
|
|
Discriminant of lattice A_n of determinant n+1.
|
|
1
| |
|
|
1, 1, -3, -2, 5, 3, -7, -4, 9, 5, -11, -6, 13, 7, -15, -8, 17, 9, -19, -10, 21, 11, -23, -12, 25, 13, -27, -14, 29, 15, -31, -16, 33, 17, -35, -18, 37, 19, -39, -20, 41, 21, -43, -22, 45, 23, -47, -24, 49, 25, -51, -26, 53, 27, -55, -28, 57, 29, -59
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,3
|
|
|
REFERENCES
| J. H. Conway, Sensual Quadratic Form, MAA, p. 4.
G. L. Watson, Integral Quadratic Forms, Camb., p. 2.
|
|
|
FORMULA
| a(2n) = (-1)^n*(2*n+1), a(2n+1) = (-1)^n*(n+1). Or (apart from signs), a(n) = n, n odd; n/2, n even.
G.f.: (1+x-x^2)/(1+x^2)^2 - Len Smiley (smiley(AT)math.uaa.alaska.edu).
a(-2-n)=(-1)^n*a(n). - Michael Somos Jun 15 2005
a(0)=1, a(1)=1, a(2)=-3, a(3)=-2, a(n)=-2*a(n-2)-a(n-4) [From Harvey P. Dale, Dec 02 2011]
|
|
|
MATHEMATICA
| CoefficientList[Series[(1+x-x^2)/(1+x^2)^2, {x, 0, 60}], x] (* or *) LinearRecurrence[{0, -2, 0, -1}, {1, 1, -3, -2}, 70]
|
|
|
PROG
| (PARI) a(n)=if(n==-1, 0, (-1)^(n\2)*(n+1)/gcd(n+1, 2)) /* Michael Somos Jun 15 2005 */
|
|
|
CROSSREFS
| A026741 is unsigned version: a(n)=(-1)^[n/2]A026741(n+1).
Sequence in context: A165342 A076605 A194748 * A176447 A145051 A026741
Adjacent sequences: A030637 A030638 A030639 * A030641 A030642 A030643
|
|
|
KEYWORD
| sign,easy,nice
|
|
|
AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
|
| |
|
|
