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A085388 First differences of n^k. 4
1, 1, 0, 1, 1, 0, 1, 2, 2, 0, 1, 3, 6, 4, 0, 1, 4, 12, 18, 8, 0, 1, 5, 20, 48, 54, 16, 0, 1, 6, 30, 100, 192, 162, 32, 0, 1, 7, 42, 180, 500, 768, 486, 64, 0, 1, 8, 56, 294, 1080, 2500, 3072, 1458, 128, 0, 1, 9, 72, 448, 2058, 6480, 12500, 12288, 4374, 256, 0, 1, 10, 90, 648 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,8
COMMENTS
T(n,k) is the number of k-digit numbers in base n; n,k >= 2. - Mohammed Yaseen, Nov 11 2022
LINKS
FORMULA
T(n,k) = (n-1)*n^(k-1) + 0^k/n. - Corrected by Mohammed Yaseen, Nov 11 2022
T(n,0) = 1; T(n,k) = n^k - n^(k-1) for k >= 1. - Mohammed Yaseen, Nov 11 2022
EXAMPLE
Rows begin
1, 0, 0, 0, 0, ...
1, 1, 2, 4, 8, ...
1, 2, 6, 18, 54, ...
1, 3, 12, 48, 192, ...
1, 4, 20, 100, 500, ...
CROSSREFS
Diagonals include A053506, A085389, A085390.
Row-wise binomial transform is A083064.
Sequence in context: A246935 A342120 A198793 * A351339 A361432 A294498
KEYWORD
easy,nonn,tabl
AUTHOR
Paul Barry, Jun 30 2003
EXTENSIONS
Offset corrected by Mohammed Yaseen, Nov 11 2022
STATUS
approved

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Last modified March 29 00:26 EDT 2024. Contains 371264 sequences. (Running on oeis4.)