|
|
A289261
|
|
Coefficients in the expansion of 1/([r]-[2r]x+[3r]x^2-...); [ ]=floor, r=13/8.
|
|
2
|
|
|
1, 3, 5, 9, 17, 30, 52, 91, 160, 281, 494, 871, 1537, 2711, 4782, 8437, 14885, 26258, 46320, 81712, 144145, 254277, 448555, 791273, 1395843, 2462330, 4343664, 7662429, 13516885, 23844416, 42062667, 74200520, 130893196, 230901729, 407321472, 718534172
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
COMMENTS
|
Conjecture: the sequence is strictly increasing.
|
|
LINKS
|
|
|
FORMULA
|
G.f.: 1/(Sum_{k>=0} [(k+1)*r)](-x)^k), where r = 13/8 and [ ] = floor.
G.f.: (1 - x)*(1 + x)^2*(1 + x^2)*(1 + x^4) / (1 - 2*x + x^2 - 2*x^3 + 2*x^4 - x^5 + 2*x^6 - 2*x^7). - Colin Barker, Jul 14 2017
|
|
MATHEMATICA
|
r = 13/8;
u = 1000; (* # initial terms from given series *)
v = 100; (* # coefficients in reciprocal series *)
CoefficientList[Series[1/Sum[Floor[r*(k + 1)] (-x)^k, {k, 0, u}], {x, 0, v}], x]
|
|
PROG
|
(PARI) Vec((1 - x)*(1 + x)^2*(1 + x^2)*(1 + x^4) / (1 - 2*x + x^2 - 2*x^3 + 2*x^4 - x^5 + 2*x^6 - 2*x^7) + O(x^50)) \\ Colin Barker, Jul 20 2017
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|