A350001 Iterated differences of lucky numbers. Array read by antidiagonals, n >= 0, k >= 1: T(0,k) = A000959(k), T(n,k) = T(n-1,k+1) - T(n-1,k) for n > 0.

1, 3, 2, 7, 4, 2, 9, 2, -2, -4, 13, 4, 2, 4, 8, 15, 2, -2, -4, -8, -16, 21, 6, 4, 6, 10, 18, 34, 25, 4, -2, -6, -12, -22, -40, -74, 31, 6, 2, 4, 10, 22, 44, 84, 158, 33, 2, -4, -6, -10, -20, -42, -86, -170, -328, 37, 4, 2, 6, 12, 22, 42, 84, 170, 340, 668

Offset

0,2

Links

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

Index entries for sequences related to lucky numbers

Formula

T(n,k) = Sum_{j=0..n} (-1)^(n-j)*binomial(n,j)*A000959(k+j).

Example

Array begins:
  n\k|    1    2    3    4    5    6    7     8    9    10   11   12
  ---+--------------------------------------------------------------
   0 |    1    3    7    9   13   15   21    25   31    33   37   43
   1 |    2    4    2    4    2    6    4     6    2     4    6    6
   2 |    2   -2    2   -2    4   -2    2    -4    2     2    0   -4
   3 |   -4    4   -4    6   -6    4   -6     6    0    -2   -4   14
   4 |    8   -8   10  -12   10  -10   12    -6   -2    -2   18  -32
   5 |  -16   18  -22   22  -20   22  -18     4    0    20  -50   56
   6 |   34  -40   44  -42   42  -40   22    -4   20   -70  106  -82
   7 |  -74   84  -86   84  -82   62  -26    24  -90   176 -188  102
   8 |  158 -170  170 -166  144  -88   50  -114  266  -364  290 -100
   9 | -328  340 -336  310 -232  138 -164   380 -630   654 -390   50
  10 |  668 -676  646 -542  370 -302  544 -1010 1284 -1044  440   78

Crossrefs

Cf. A000959 (row n = 0), A031883 (row n = 1), A123593 (column k = 1).

Cf. A254967 (absolute differences), A095195 (iterated differences of primes), A350004 (iterated differences of ludic numbers).

Sequence in context: A198501 A230072 A345947 * A344969 A011772 A060451

Adjacent sequences: A349998 A349999 A350000 * A350002 A350003 A350004

Keyword

sign,tabl

Author

Pontus von Brömssen, Dec 08 2021

Status

approved