|
|
A189144
|
|
a(n) = lcm(n,n+1,n+2,n+3,n+4,n+5,n+6)/420.
|
|
2
|
|
|
0, 1, 2, 6, 6, 66, 66, 858, 858, 429, 572, 9724, 2652, 50388, 3876, 3876, 42636, 245157, 28842, 48070, 32890, 296010, 296010, 780390, 33930, 525915, 841464, 712008, 1344904, 1344904, 139128
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,3
|
|
COMMENTS
|
(n-1)!*12600*a(n)/(n+6)! produces a sequence of fractions(from offset 1).
The numerators have a period of 5, repeating [5,5,5,1,1]=4*(n^4 mod 5 +(n-1)^4 mod 5 -1)+1
The denominators have a period of 12, repeating[2,8,12,8,2,24,4,8,6,8,4,24]. This sequence factors to 2^(p(n)*3^q(n) where p(n)is a sequence of period 4,repeating [1,3,2,3] and q(n) is a sequence of period 3, repeating[0,0,1]. p(n)= A131729(n+1)+2.q(n)=A022003(n-1)
|
|
LINKS
|
|
|
FORMULA
|
a(n)= (n+6)!*f(n)/(12600*(n-1)!*2^p(n)*3^q(n)),n>0 where
f(n)= 4*(n^4 mod 5 +(n-1)^4 mod 5 -1)+1
p(n)=(9+2*cos((n-3)*Pi/2)+3*(-1)^n)/4
q(n)=((n-1)^5 -(n-1)^2) mod 3
|
|
MAPLE
|
seq(lcm(n, n+1, n+2, n+3, n+4, n+5, n+6)/420, n=0..30);
f:= n-> 4*(n^4 mod 5 +(n-1)^4 mod 5 -1)+1:p:= n->)=(9+2*cos((n-3)*Pi/2)+3*(-1)^n)/4:q:=n->)=((n-1)^5 -(n-1)^2) mod 3: seq((n+6)!*f(n)/(12600*(n-1)!*2^p(n)*3^q(n)), n=1..30);
|
|
MATHEMATICA
|
Table[(LCM@@Range[n, n+6])/420, {n, 0, 30}] (* Harvey P. Dale, Jun 13 2015 *)
|
|
PROG
|
(Haskell)
a189144 n = (foldl1 lcm [n..n+6]) `div` 420
|
|
CROSSREFS
|
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|