|
Search: id:A144732
|
|
|
| A144732 |
|
Triangle of numerator coefficients, reading across rows, of Sum[1/(1+r^2-2rCos[k Pi/n])], k from 1 to n. n=1: 1/(1+r+r^2). n=2: 2+2r+2r^2/(2*(1+2r+2r^2+2r^3+r^4)).[Omitting powers of variable]n=3: 3 4 5 4 3/(3*(1 2 2 2 2 2 1). Diagonals of the triangle of numerators have differences of 1, then 2, then 3, ..., etc. |
|
+0
1
|
|
| 1, 2, 2, 2, 3, 4, 5, 4, 3, 4, 6, 8, 8, 8, 6, 4, 5, 8, 11, 12, 13, 12, 11, 8, 5
(list; graph; listen)
|
|
|
OFFSET
|
1,2
|
|
|
COMMENT
|
Conjecture: In limit as n->Infinity the sum = 1/(1-r^2), 0<r<1. Cf. Poisson integral.
|
|
LINKS
|
Poisson Integral
|
|
FORMULA
|
Numerators/denominators: 1/((121)x1); 222/((12221)x2); 34543/((1222221)x3); 4688864 / ((122222221)x4)...etc.
|
|
EXAMPLE
|
n=5: 5+8r+11r^2+12r^3+13r^4+12r^5+11r^6+8r^7+5r^8 /(5*(1+2r+2r^2+2r^3+2r^4+2r^5+2r^6+2r^7+2r^8+2r^9+r^10))
|
|
MATHEMATICA
|
Sum[1/(1+r^2-2rCos[Pi*k/n]), {k, 1, n}]
|
|
CROSSREFS
|
Sequence in context: A015740 A015750 A084848 this_sequence A055224 A126295 A162352
Adjacent sequences: A144729 A144730 A144731 this_sequence A144733 A144734 A144735
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Daniel Tisdale (daniel6874(AT)gmail.com), Sep 20 2008
|
|
|
Search completed in 0.002 seconds
|
