A095145 Triangle, read by rows, formed by reading Pascal's triangle (A007318) mod 12.

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

Offset

0,5

Links

Table of n, a(n) for n=0..104.

Ilya Gutkovskiy, Illustrations (triangle formed by reading Pascal's triangle mod m)

Index entries for triangles and arrays related to Pascal's triangle

Formula

T(i, j) = binomial(i, j) mod 12.

Mathematica

Mod[ Flatten[ Table[ Binomial[n, k], {n, 0, 13}, {k, 0, n}]], 12]

Prog

(Python)
# uses python code from A034931 and A083093
from sympy.ntheory.modular import crt
def A095145(n): return crt([4, 3], [A034931(n), A083093(n)])[0] # Chai Wah Wu, Jul 19 2025

Crossrefs

Cf. A007318, A047999, A083093, A034931, A095140, A095141, A095142, A034930, A095143, A008975, A095144, A034932.

Sequences based on the triangles formed by reading Pascal's triangle mod m: A047999 (m = 2), A083093 (m = 3), A034931 (m = 4), A095140 (m = 5), A095141 (m = 6), A095142 (m = 7), A034930 (m = 8), A095143 (m = 9), A008975 (m = 10), A095144 (m = 11), (this sequence) (m = 12), A275198 (m = 14), A034932 (m = 16).

Sequence in context: A061676 A180182 A275198 * A095144 A339359 A144398

Adjacent sequences: A095142 A095143 A095144 * A095146 A095147 A095148

Keyword

easy,nonn,tabl

Author

Robert G. Wilson v, May 29 2004

Status

approved