A089651 -id:A089651 - cp's OEIS frontend

A089606 Table T(n,k), n>=1 and k>=1; the k-th row is defined by :partial sums of the sequence 1, a(1), .., a(1), a(2), .., a(2), a(3), ..,a(3), a(4), ... each term repeated k times (with a(i)= T(i,k)).

1, 2, 1, 4, 2, 1, 8, 3, 2, 1, 16, 5, 3, 2, 1, 32, 7, 4, 3, 2, 1, 64, 10, 6, 4, 3, 2, 1, 128, 13, 8, 5, 4, 3, 2, 1, 256, 18, 10, 7, 5, 4, 3, 2, 1, 512, 23, 13, 9, 6, 5, 4, 3, 2, 1, 1024, 30, 16, 11, 8, 6, 5, 4, 3, 2, 1, 2048, 37, 19, 13, 10, 7, 6, 5, 4, 3, 2, 1

Offset: 1

Philippe Deléham, Jan 03 2004

Row k=1 : 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, ...
Row k=2 : 1, 2, 3, 5,  7, 10, 13,  18,  23,  30,   37,   47, ...
Row k=3 : 1, 2, 3, 4,  6,  8, 10,  13,  16,  19,   23,   27, ...
Row k=4 : 1, 2, 3, 4,  5,  7,  9,  11,  13,  16,   19,   22, ...
Row k=5 : 1, 2, 3, 4,  5,  6,  8,  10,  12,  14,   16,   19, ...

Alois P. Heinz, First 200 antidiagonals, flattened

Cf. A000079, A033485, A089649, A089651.

T:= proc(n, k) option remember; `if`(n=1, 1,
      T(n-1, k)+T(floor((n+k-2)/k), k))
    end:
seq(seq(T(1+d-k,k), k=1..d), d=1..12);  # Alois P. Heinz, Feb 24 2023

T(n,1) = A000079(n-1) = 2^(n-1).
T(n,2) = A033485(n).
T(n,3) = A089649(n).
T(n,4) = A089651(n).

cp's OEIS Frontend

A089606 Table T(n,k), n>=1 and k>=1; the k-th row is defined by :partial sums of the sequence 1, a(1), .., a(1), a(2), .., a(2), a(3), ..,a(3), a(4), ... each term repeated k times (with a(i)= T(i,k)).

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