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 A034931 Pascal's triangle read modulo 4. 23
 1, 1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 0, 2, 0, 1, 1, 1, 2, 2, 1, 1, 1, 2, 3, 0, 3, 2, 1, 1, 3, 1, 3, 3, 1, 3, 1, 1, 0, 0, 0, 2, 0, 0, 0, 1, 1, 1, 0, 0, 2, 2, 0, 0, 1, 1, 1, 2, 1, 0, 2, 0, 2, 0, 1, 2, 1, 1, 3, 3, 1, 2, 2, 2, 2, 1, 3, 3, 1, 1, 0, 2, 0, 3, 0, 0, 0, 3, 0, 2, 0, 1, 1, 1, 2, 2, 3, 3, 0, 0, 3, 3, 2, 2, 1, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS The number of 3's in row n is given by 2^(A000120(n)-1) if A014081(n) is nonzero, else by 0 [Davis & Webb]. - R. J. Mathar, Jul 28 2017 LINKS Reinhard Zumkeller, Rows n = 0..120 of triangle, flattened Kenneth S. Davis and William A. Webb, Lucas' theorem for prime powers, European Journal of Combinatorics 11:3 (1990), pp. 229-233. Kenneth S. Davis and William A. Webb, Pascal's triangle modulo 4, Fib. Quart., 29 (1991), 79-83. James G. Huard, Blair K. Spearman, and Kenneth S. Williams, Pascal's triangle (mod 8), European Journal of Combinatorics 19:1 (1998), pp. 45-62. Ivan Korec, Definability of Pascal's Triangles Modulo 4 and 6 and Some Other Binary Operations from Their Associated Equivalence Relations, Acta Univ. M. Belii Ser. Math. 4 (1996), pp. 53-66. FORMULA T(n+1,k) = (T(n,k) + T(n,k-1)) mod 4. - Reinhard Zumkeller, Mar 14 2015 EXAMPLE Triangle begins:   {1},   {1, 1},   {1, 2, 1},   {1, 3, 3, 1},   {1, 0, 2, 0, 1},   {1, 1, 2, 2, 1, 1},   {1, 2, 3, 0, 3, 2, 1},   {1, 3, 1, 3, 3, 1, 3, 1},   {1, 0, 0, 0, 2, 0, 0, 0, 1},   {1, 1, 0, 0, 2, 2, 0, 0, 1, 1},   {1, 2, 1, 0, 2, 0, 2, 0, 1, 2, 1},   {1, 3, 3, 1, 2, 2, 2, 2, 1, 3, 3, 1},   ... MAPLE A034931 := proc(n, k)     modp(binomial(n, k), 4) ; end proc: seq(seq(A034931(n, k), k=0..n), n=0..10); # R. J. Mathar, Jul 28 2017 MATHEMATICA Mod[ Flatten[ Table[ Binomial[n, k], {n, 0, 13}, {k, 0, n}]], 4] (* Robert G. Wilson v, May 26 2004 *) PROG (Haskell) a034931 n k = a034931_tabl !! n !! k a034931_row n = a034931_tabl !! n a034931_tabl = iterate    (\ws -> zipWith ((flip mod 4 .) . (+)) ([0] ++ ws) (ws ++ [0])) [1] -- Reinhard Zumkeller, Mar 14 2015 (PARI) C(n, k)=binomial(n, k)%4 \\ Charles R Greathouse IV, Aug 09 2016 (PARI) f(n, k)=2*(bitand(n-k, k)==0); T(n, j)=if(j==0, return(1)); my(k=logint(n, 2), K=2^k, K1=K/2, L=n-K); if(L

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Last modified December 11 02:13 EST 2019. Contains 329910 sequences. (Running on oeis4.)