A350001 - OEIS

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

(list; table; graph; refs; listen; history; text; internal format)

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