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A225043 Pascal's triangle with row n reduced modulo n+1. 3
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

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

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

FORMULA

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

EXAMPLE

{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},...

MATHEMATICA

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

PROG

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

(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

CROSSREFS

Cf. A007318, A062173, A001803, A086117.

Sequence in context: A095141 A177974 A095140 * A125605 A110570 A082905

Adjacent sequences:  A225040 A225041 A225042 * A225044 A225045 A225046

KEYWORD

nonn,tabl

AUTHOR

Roger L. Bagula, Apr 25 2013

EXTENSIONS

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

STATUS

approved

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Last modified March 25 03:50 EDT 2019. Contains 321450 sequences. (Running on oeis4.)