OFFSET
0,1
COMMENTS
Row k is the k-th differences of A013929.
FORMULA
A(i,j) = sum_{k=0..j} (-1)^(j-k) binomial(j,k) A013929(i+k).
EXAMPLE
Array form:
n=1: n=2: n=3: n=4: n=5: n=6: n=7: n=8: n=9:
---------------------------------------------------------
k=0: 4 8 9 12 16 18 20 24 25
k=1: 4 1 3 4 2 2 4 1 2
k=2: -3 2 1 -2 0 2 -3 1 -1
k=3: 5 -1 -3 2 2 -5 4 -2 4
k=4: -6 -2 5 0 -7 9 -6 6 -7
k=5: 4 7 -5 -7 16 -15 12 -13 10
k=6: 3 -12 -2 23 -31 27 -25 23 -13
k=7: -15 10 25 -54 58 -52 48 -36 13
k=8: 25 15 -79 112 -110 100 -84 49 1
k=9: -10 -94 191 -222 210 -184 133 -48 -57
Triangle form:
4
8 4
9 1 -3
12 3 2 5
16 4 1 -1 -6
18 2 -2 -3 -2 4
20 2 0 2 5 7 3
24 4 2 2 0 -5 -12 -15
25 1 -3 -5 -7 -7 -2 10 25
27 2 1 4 9 16 23 25 15 -10
28 1 -1 -2 -6 -15 -31 -54 -79 -94 -84
32 4 3 4 6 12 27 58 112 191 285 369
MATHEMATICA
nn=9;
t=Table[Take[Differences[NestList[NestWhile[#+1&, #+1, SquareFreeQ[#]&]&, 4, 2*nn], k], nn], {k, 0, nn}]
Table[t[[j, i-j+1]], {i, nn}, {j, i}]
CROSSREFS
KEYWORD
AUTHOR
Gus Wiseman, Oct 19 2024
STATUS
approved