cp's OEIS Frontend

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.

%I A350004 #8 Oct 29 2023 20:31:23
%S A350004 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,
%T A350004 4,2,4,8,14,23,37,23,6,2,0,-4,-12,-26,-49,-86,25,2,-4,-6,-6,-2,10,36,
%U A350004 85,171,29,4,2,6,12,18,20,10,-26,-111,-282
%N 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.
%H A350004 Winston de Greef, <a href="/A350004/b350004.txt">Table of n, a(n) for n = 0..11324</a> (150 antidiagonals)
%F A350004 T(n,k) = Sum_{j=0..n} (-1)^(n-j)*binomial(n,j)*A003309(k+j).
%e A350004 Array begins:
%e A350004   n\k|    1    2    3   4    5   6    7    8   9   10
%e A350004   ---+-----------------------------------------------
%e A350004    0 |    1    2   3    5    7  11   13   17  23   25
%e A350004    1 |    1    1   2    2    4   2    4    6   2    4
%e A350004    2 |    0    1   0    2   -2   2    2   -4   2    4
%e A350004    3 |    1   -1   2   -4    4   0   -6    6   2   -8
%e A350004    4 |   -2    3  -6    8   -4  -6   12   -4 -10   10
%e A350004    5 |    5   -9  14  -12   -2  18  -16   -6  20   -8
%e A350004    6 |  -14   23 -26   10   20 -34   10   26 -28    2
%e A350004    7 |   37  -49  36   10  -54  44   16  -54  30    8
%e A350004    8 |  -86   85 -26  -64   98 -28  -70   84 -22  -26
%e A350004    9 |  171 -111 -38  162 -126 -42  154 -106  -4   64
%e A350004   10 | -282   73 200 -288   84 196 -260  102  68 -142
%Y A350004 Cf. A003309 (row n = 0), A260723 (row n = 1).
%Y A350004 Cf. A095195 (iterated differences of primes), A350001 (iterated differences of lucky numbers).
%K A350004 sign,tabl
%O A350004 0,2
%A A350004 _Pontus von Brömssen_, Dec 08 2021