A225043 Pascal's triangle with row n reduced modulo n+1.

0, 1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 4, 1, 4, 1, 1, 5, 4, 4, 5, 1, 1, 6, 1, 6, 1, 6, 1, 1, 7, 5, 3, 3, 5, 7, 1, 1, 8, 1, 2, 7, 2, 1, 8, 1, 1, 9, 6, 4, 6, 6, 4, 6, 9, 1, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 1, 11, 7, 9, 6, 6, 6, 6, 9, 7, 11, 1, 1, 12, 1, 12, 1, 12, 1, 12, 1, 12, 1, 12, 1

Offset: 0

Author

Roger L. Bagula, Apr 25 2013

Keywords

• nonn
• tabl

Comments

The row sums are: {0, 2, 4, 8, 11, 20, 22, 32, 31, 52, 56, ...}.

Since row n is only defined mod n+1, it would seem better to reduce the row sums mod n+1, which gives A062173. - N. J. A. Sloane, Apr 28 2013

Examples

			{0},
{1, 1},
{1, 2, 1},
{1, 3, 3, 1},
{1, 4, 1, 4, 1},
{1, 5, 4, 4, 5, 1},
{1, 6, 1, 6, 1, 6, 1},
{1, 7, 5, 3, 3, 5, 7, 1},
{1, 8, 1, 2, 7, 2, 1, 8, 1},
{1, 9, 6, 4, 6, 6, 4, 6, 9, 1},
{1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1},
{1, 11, 7, 9, 6, 6, 6, 6, 9, 7, 11, 1},
{1, 12, 1, 12, 1, 12, 1, 12, 1, 12, 1, 12, 1},...
		

Links

• Reinhard Zumkeller, Rows n = 0..120 of triangle, flattened
• Eric Weisstein's World of Mathematics, Binomial Distribution
• Index entries for triangles and arrays related to Pascal's triangle

Crossrefs

Cf. A007318, A062173, A001803, A086117.

Programs

Haskell

a225043 n k = a225043_tabl !! n !! k
a225043_row n = a225043_tabl !! n
a225043_tabl = zipWith (map . flip mod) [1..] a007318_tabl
-- Reinhard Zumkeller, Jun 12 2013

Mathematica

Flatten[Table[Mod[Binomial[m, n], m + 1], {m, 0, 12}, {n, 0, m}]]

PARI

T(m,n)=binomial(m,n)%(m+1) \\ Charles R Greathouse IV, Apr 25 2013

Formula

T(m,n) = binomial(m, n) mod m+1.

Extensions

Definition edited by N. J. A. Sloane, Apr 28 2013