OFFSET
1,3
COMMENTS
These are the numbers k such that mean of the numbers in the first k rows of Pascal' s triangle is an integer. All such k except 1 are congruent to -1 mod 6.
LINKS
Robert Israel, Table of n, a(n) for n = 1..181
EXAMPLE
The sum of the numbers in Pascal's triangle, from row 0 through row 17, is 2^18 - 1 = 262143; the number of such numbers is C(19,2) = 171, and 262143/171 = 1533; thus 17 is in this sequence, and 1533 is in A246637.
MAPLE
select(k -> 2 &^(k+1) - 1 mod ((k+1)*(k+2)/2) = 0, [$0..10^6]); # Robert Israel, Nov 30 2023
MATHEMATICA
z = 1000;
t = Select[Range[0, z], IntegerQ[(2^(# + 1) - 1)/Binomial[# + 2, 2]] &]
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Sep 01 2014
EXTENSIONS
Offset corrected by Robert Israel, Nov 30 2023
STATUS
approved