A174680 Numerator of 1/16 - 1/n^2, using -1 at the pole where n=0.

-1, -15, -3, -7, 0, 9, 5, 33, 3, 65, 21, 105, 1, 153, 45, 209, 15, 273, 77, 345, 3, 425, 117, 513, 35, 609, 165, 713, 3, 825, 221, 945, 63, 1073, 285, 1209, 5, 1353, 357, 1505, 99, 1665, 437, 1833, 15, 2009, 525, 2193, 143, 2385, 621, 2585, 21, 2793, 725, 3009, 195, 3233, 837, 3465, 14, 3705

Offset

0,2

Comments

Extends the Brackett spectrum to negative principal quantum numbers in the spirit of A144477 and A171709.

Links

G. C. Greubel, Table of n, a(n) for n = 0..10000

Formula

a(n) = A061041(n), n >= 4.

a(n) = A172157(4,n), n >= 1.

a(n) = a(-n) for all n in Z.

Mathematica

Table[(n^2 - 16)/(GCD[n^2 - 16, 16*n^2]), {n, 0, 100}] (* G. C. Greubel, Sep 16 2018 *)

Prog

(PARI) {a(n) = (n^2 - 16) / gcd(n^2 - 16, 16 * n^2)}; /* Michael Somos, Jan 06 2011 */

Crossrefs

Cf. A174233, A067998.

Sequence in context: A040218 A226379 A037924 * A225948 A248129 A256527

Adjacent sequences: A174677 A174678 A174679 * A174681 A174682 A174683

Keyword

sign,easy

Author

Paul Curtz, Nov 30 2010

Extensions

removed a(-4)-a(-1) since a(-n)=a(n) by Michael Somos, Jan 06 2011

Status

approved