|
|
A182753
|
|
Expansion of (1 + 14*x)/(1 - 35*x^2).
|
|
6
|
|
|
1, 14, 35, 490, 1225, 17150, 42875, 600250, 1500625, 21008750, 52521875, 735306250, 1838265625, 25735718750, 64339296875, 900750156250, 2251875390625, 31526255468750, 78815638671875, 1103418941406250, 2758547353515625, 38619662949218750, 96549157373046875
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
COMMENTS
|
a(1) = 1, a(2) = 14, for n >= 3; a(n) = the smallest number h > a(n-1) such that [[a(n-2) + a(n-1)] * [a(n-2) + h] * [a(n-1) + h]] / [a(n-2) * a(n-1) * h] is integer (= 54).
|
|
LINKS
|
|
|
FORMULA
|
a(2n) = 14 * a(2n-1), a(2n+1) = 5/2 * a(2n).
a(2n) = 14*35^(n-1), a(2n+1) = 35^n.
|
|
EXAMPLE
|
For n = 5; a(3) = 35, a(4) = 490, a(5) = 1225 before [(35+490)*(35+1225)*(490+1225)] / (35*490*1225) = 54.
|
|
MATHEMATICA
|
LinearRecurrence[{0, 35}, {1, 14}, 30] (* or *) CoefficientList[Series[(1 + 14*x)/(1-35*x^2), {x, 0, 50}], x] (* G. C. Greubel, Jan 11 2018 *)
|
|
PROG
|
(Magma) I:=[1, 14]; [n le 2 select I[n] else 35*Self(n-2): n in [1..30]]; // G. C. Greubel, Jan 11 2018
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|