A268681 Sum of unique squarefree numbers in first n rows of Pascal's triangle.

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

Offset

1,3

Links

Peter Kagey, Table of n, a(n) for n = 1..250

Project Euler, Problem 203: Squarefree Binomial Coefficients

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

Cf. A005117, A007318.

Sequence in context: A135035 A054195 A054190 * A101013 A088688 A290997

Adjacent sequences: A268678 A268679 A268680 * A268682 A268683 A268684

Keyword

nonn

Author

Peter Kagey, Feb 10 2016

Status

approved