A094497 Triangular table A(n,j) = C(n,j) - C(n,j) mod n^3, difference of binomial coefficient and its residue mod n^3, read by rows.

1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2744, 2744, 2744, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3375, 3375, 3375, 3375, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4096, 4096, 8192, 12288, 8192, 4096, 4096

Offset: 0

Author

Labos Elemer, Jun 02 2004

Keywords

• easy
• nonn
• tabl

Comments

a(0) = 1 by convention.

Examples

			Out of a(1)=1 and a(2)=1, the first deviation from A007318 is at a(111) because C(14,6) = 3003, 3003 mod 2744 = 259, a(111) = 2744.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 0..10439; the first 144 rows of triangle
• Index entries for triangles and arrays related to Pascal's triangle

Crossrefs

Cf. A007318, A053200, A094495, A094496.

Programs

Mathematica

Flatten[Table[Table[Binomial[n, j]-Mod[Binomial[n, j], n^3], {j, 0, n}], {n, 1, 14}], 1]