A350004 - OEIS

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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

(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)

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