|
|
A008732
|
|
Molien series for 3-dimensional group [2,n] = *22n.
|
|
10
|
|
|
1, 2, 3, 4, 5, 7, 9, 11, 13, 15, 18, 21, 24, 27, 30, 34, 38, 42, 46, 50, 55, 60, 65, 70, 75, 81, 87, 93, 99, 105, 112, 119, 126, 133, 140, 148, 156, 164, 172, 180, 189, 198, 207, 216, 225, 235, 245, 255, 265
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
LINKS
|
|
|
FORMULA
|
a(n) = floor( (n+3)*(n+4)/10 ) = (n+2)*(n+5)/10 + b(n)/5 where b(n) = A010891(n-2) + 2*A092202(n-1) = 0, 1, 1, 0, -2, ... with period length 5.
G.f.: 1/((1-x)^2*(1-x^5)).
a(n) = Sum_{j=0..n+5} floor(j/5).
a(n-5) = (1/2)floor(n/5)*(2*n - 3 - 5*floor(n/5)). (End)
|
|
EXAMPLE
|
Stored in five columns:
1 2 3 4 5
7 9 11 13 15
18 21 24 27 30
34 38 42 46 50
55 60 65 70 75
81 87 93 99 105
112 119 126 133 140
(End)
|
|
MAPLE
|
A092202 := proc(n) op(1+(n mod 5), [0, 1, 0, -1, 0]) ; end proc:
A010891 := proc(n) op(1+(n mod 5), [1, -1, 0, 0, 0]) ; end proc:
|
|
MATHEMATICA
|
LinearRecurrence[{2, -1, 0, 0, 1, -2, 1}, {1, 2, 3, 4, 5, 7, 9}, 50] (* Jean-François Alcover, Jan 18 2018 *)
|
|
PROG
|
(Sage) [floor((n+3)*(n+4)/10) for n in (0..50)] # G. C. Greubel, Jul 30 2019
(GAP) List([0..50], n-> Int((n+3)*(n+4)/10)); # G. C. Greubel, Jul 30 2019
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy,tabf
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|