|
|
A268681
|
|
Sum of unique squarefree numbers in first n rows of Pascal's triangle.
|
|
1
|
|
|
1, 1, 3, 6, 12, 27, 42, 105, 175, 175, 385, 1408, 1474, 2566, 8677, 15607, 15607, 39934, 39934, 133300, 264305, 559565, 1288392, 5482695, 5493321, 5546451, 11088442, 11088442, 24211552, 88854292, 88854757, 133243378, 133243378, 133243411, 2337205436
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,3
|
|
LINKS
|
|
|
EXAMPLE
|
a(5) = 1 + 2 + 3 + 6 = 12 because the squarefree numbers in the first 5 rows of Pascal's triangle are 1, 2, 3, and 6:
1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
|
|
MATHEMATICA
|
lim = 35; t = Select[#, SquareFreeQ] & /@ Table[Binomial[n, k], {n, 0, lim}, {k, 0, n}]; Table[Total@ Union[Flatten@ Take[t, n]], {n, lim}] (* Michael De Vlieger, Feb 11 2016 *)
|
|
PROG
|
(PARI) row(n) = vector(n, k, k--; binomial(n-1, k));
sqfrow(n) = select(x->issquarefree(x), row(n));
lista(nn) = {my(s = 0, vsqf = []); for (n=1, nn, vsqf = concat(vsqf, sqfrow(n)); vsqf = vecsort(vsqf, , 8); print1(vecsum(vsqf), ", "); ); } \\ Michel Marcus, Feb 11 2016
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|