A365644 Array read by ascending antidiagonals: A(n, k) = k*(10^n - 1)/9 with k >= 0.

0, 0, 0, 0, 1, 0, 0, 11, 2, 0, 0, 111, 22, 3, 0, 0, 1111, 222, 33, 4, 0, 0, 11111, 2222, 333, 44, 5, 0, 0, 111111, 22222, 3333, 444, 55, 6, 0, 0, 1111111, 222222, 33333, 4444, 555, 66, 7, 0, 0, 11111111, 2222222, 333333, 44444, 5555, 666, 77, 8, 0

Offset

0,8

Links

Table of n, a(n) for n=0..54.

Formula

O.g.f.: x*y/((1 - x)*(1 - 10*x)*(1 - y)^2).

E.g.f.: y*exp(x+y)*(exp(9*x) - 1)/9.

A(n, 11) = A132583(n-1) for n > 0.

A(n, 12) = A073551(n+1) for n > 0.

Example

The array begins:
  0,     0,     0,     0,     0,     0, ...
  0,     1,     2,     3,     4,     5, ...
  0,    11,    22,    33,    44,    55, ...
  0,   111,   222,   333,   444,   555, ...
  0,  1111,  2222,  3333,  4444,  5555, ...
  0, 11111, 22222, 33333, 44444, 55555, ...
  ...

Mathematica

A[n_, k_]:=k(10^n-1)/9; Table[A[n-k, k], {n, 0, 9}, {k, 0, n}]//Flatten

Crossrefs

Cf. A000004 (n=0 or k=0), A001477 (n=1), A002275 (k=1), A002276 (k=2), A002277 (k=3), A002278 (k=4), A002279 (k=5), A002280 (k=6), A002281 (k=7), A002282 (k=8), A002283 (k=9), A008593 (n=2), A053422 (main diagonal), A105279 (k=10), A132583, A177769 (n=3), A365645 (antidiagonal sums), A365646.

Sequence in context: A204848 A027645 A193925 * A010190 A323454 A261353

Adjacent sequences: A365641 A365642 A365643 * A365645 A365646 A365647

Keyword

nonn,base,easy,tabl

Author

Stefano Spezia, Sep 14 2023

Status

approved