A350004 Iterated differences of ludic numbers. Array read by antidiagonals, n >= 0, k >= 1: T(0,k) = A003309(k), T(n,k) = T(n-1,k+1)-T(n-1,k) for n > 0.

1, 2, 1, 3, 1, 0, 5, 2, 1, 1, 7, 2, 0, -1, -2, 11, 4, 2, 2, 3, 5, 13, 2, -2, -4, -6, -9, -14, 17, 4, 2, 4, 8, 14, 23, 37, 23, 6, 2, 0, -4, -12, -26, -49, -86, 25, 2, -4, -6, -6, -2, 10, 36, 85, 171, 29, 4, 2, 6, 12, 18, 20, 10, -26, -111, -282

Offset

0,2

Links

Winston de Greef, Table of n, a(n) for n = 0..11324 (150 antidiagonals)

Formula

T(n,k) = Sum_{j=0..n} (-1)^(n-j)*binomial(n,j)*A003309(k+j).

Example

Array begins:
  n\k|    1    2    3   4    5   6    7    8   9   10
  ---+-----------------------------------------------
   0 |    1    2   3    5    7  11   13   17  23   25
   1 |    1    1   2    2    4   2    4    6   2    4
   2 |    0    1   0    2   -2   2    2   -4   2    4
   3 |    1   -1   2   -4    4   0   -6    6   2   -8
   4 |   -2    3  -6    8   -4  -6   12   -4 -10   10
   5 |    5   -9  14  -12   -2  18  -16   -6  20   -8
   6 |  -14   23 -26   10   20 -34   10   26 -28    2
   7 |   37  -49  36   10  -54  44   16  -54  30    8
   8 |  -86   85 -26  -64   98 -28  -70   84 -22  -26
   9 |  171 -111 -38  162 -126 -42  154 -106  -4   64
  10 | -282   73 200 -288   84 196 -260  102  68 -142

Crossrefs

Cf. A003309 (row n = 0), A260723 (row n = 1).

Cf. A095195 (iterated differences of primes), A350001 (iterated differences of lucky numbers).

Sequence in context: A199056 A377038 A376682 * A144966 A320000 A119805

Adjacent sequences: A350001 A350002 A350003 * A350005 A350006 A350007

Keyword

sign,tabl

Author

Pontus von Brömssen, Dec 08 2021

Status

approved