cp's OEIS Frontend

A306534 Square array A(n,k), n >= 0, k >= 1, read by antidiagonals: A(n,k) = Sum_{j=0..n} floor(n/k^j).

%I A306534 #7 Feb 22 2019 05:17:17
%S A306534 0,0,2,0,1,6,0,1,3,12,0,1,2,4,20,0,1,2,4,7,30,0,1,2,3,5,8,42,0,1,2,3,
%T A306534 5,6,10,56,0,1,2,3,4,6,8,11,72,0,1,2,3,4,6,7,9,15,90,0,1,2,3,4,5,7,8,
%U A306534 10,16,110,0,1,2,3,4,5,7,8,10,13,18,132,0,1,2,3,4,5,6,8,9,11,14,19,156
%N A306534 Square array A(n,k), n >= 0, k >= 1, read by antidiagonals: A(n,k) = Sum_{j=0..n} floor(n/k^j).
%F A306534 G.f. of column k (for k > 1): (1/(1 - x)) * Sum_{j>=0} x^(k^j)/(1 - x^(k^j)).
%e A306534 Square array begins:
%e A306534    0,  0,  0,  0,  0,  0,  ...
%e A306534    2,  1,  1,  1,  1,  1,  ...
%e A306534    6,  3,  2,  2,  2,  2,  ...
%e A306534   12,  4,  4,  3,  3,  3,  ...
%e A306534   20,  7,  5,  5,  4,  4,  ...
%e A306534   30,  8,  6,  6,  6,  5,  ...
%t A306534 Table[Function[k, Sum[Floor[n/k^j], {j, 0, n}]][i - n + 1], {i, 0, 12}, {n, 0, i}] // Flatten
%Y A306534 Columns k=1..4 give A002378, A005187, A004128, A087069.
%Y A306534 Cf. A306533.
%K A306534 nonn,tabl
%O A306534 0,3
%A A306534 _Ilya Gutkovskiy_, Feb 22 2019