A361475 Array read by ascending antidiagonals: A(n, k) = (k^n - 1)/(k - 1), with k >= 2.

0, 1, 0, 3, 1, 0, 7, 4, 1, 0, 15, 13, 5, 1, 0, 31, 40, 21, 6, 1, 0, 63, 121, 85, 31, 7, 1, 0, 127, 364, 341, 156, 43, 8, 1, 0, 255, 1093, 1365, 781, 259, 57, 9, 1, 0, 511, 3280, 5461, 3906, 1555, 400, 73, 10, 1, 0, 1023, 9841, 21845, 19531, 9331, 2801, 585, 91, 11, 1, 0

Offset

0,4

Links

Table of n, a(n) for n=0..65.

Formula

E.g.f. of column k: exp(x)*(exp((k-1)*x) - 1)/(k - 1).

E.g.f. of column k: 2*exp((k+1)*x/2)*sinh((k-1)*x/2)/(k - 1).

A(n, k) = Sum_{i=0..n-1} k^i.

Example

The array begins:
   0,  0,  0,   0,   0, ...
   1,  1,  1,   1,   1, ...
   3,  4,  5,   6,   7, ...
   7, 13, 21,  31,  43, ...
  15, 40, 85, 156, 259, ...
  ...

Mathematica

A[n_, k_]:=(k^n-1)/(k-1); Flatten[Table[A[n-k+2, k], {n, 0, 10}, {k, 2, n+2}]]

Crossrefs

Cf. A003992, A361291 (k=2*n+1), A361476 (antidiagonal sums).

Cf. A000225 (k=2), A003462 (k=3), A002450 (k=4), A003463 (k=5), A003464 (k=6), A023000 (k=7), A023001 (k=8), A002452 (k=9), A002275 (k=10), A016123 (k=11).

Sequence in context: A010601 A176108 A110504 * A111246 A206306 A178124

Adjacent sequences: A361472 A361473 A361474 * A361476 A361477 A361478

Keyword

nonn,tabl

Author

Stefano Spezia, Mar 13 2023

Status

approved