OFFSET
1,2
COMMENTS
T(n, 1) = A000217(n).
T(n, 2) = A051679(n - 1) for n > 0.
From Robert Israel, Feb 26 2016: (Start)
If p is prime, T(n,p) is the number of pairs (i,j) with 0 < i < j < n such that some base-p digit of i exceeds the corresponding base-p digit of j.
If p is prime, T(n*p,p) = (p*(p+1)/2)*T(n,p) + p*(p-1)*n*(n-1)/4. (End)
LINKS
Robert Israel, Table of n, a(n) for n = 1..10011 (rows 1 to 141, flattened)
EXAMPLE
Triangle begins:
1
3 0
6 1 0
10 1 2 0
15 4 3 2 0
21 6 3 2 4 1
28 9 7 3 7 3 0
36 9 9 3 9 3 6 0
T(5, 2) = 4 because the first five rows of Pascal's triangle have 4 entries divisible by 2: one entry in the third row, and three entries in the fifth row.
1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
MAPLE
T:= (n, k) -> numboccur([seq(seq(binomial(m, j) mod k, j=0..m), m=0..n-1)], 0):
seq(seq(T(n, k), k=1..n), n=1..10); # Robert Israel, Feb 26 2016
PROG
(PARI) T(n, k) = sum(m=0, n-1, sum(j=0, m, (binomial(m, j) % k) == 0)); \\ Michel Marcus, Feb 23 2016
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Peter Kagey, Feb 16 2016
STATUS
approved