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A249732 Number of (not necessarily distinct) multiples of 4 on row n of Pascal's triangle. 6

%I

%S 0,0,0,0,2,0,1,0,6,4,3,0,7,2,3,0,14,12,11,8,13,6,7,0,19,14,11,4,17,6,

%T 7,0,30,28,27,24,29,22,23,16,33,26,23,12,29,14,15,0,43,38,35,28,37,22,

%U 23,8,45,34,27,12,37,14,15,0,62,60,59,56,61,54,55,48,65,58,55,44,61,46,47,32

%N Number of (not necessarily distinct) multiples of 4 on row n of Pascal's triangle.

%C a(n) = Number of zeros on row n of A034931 (Pascal's triangle reduced modulo 4).

%C This should have a formula (see A048967).

%H Antti Karttunen, <a href="/A249732/b249732.txt">Table of n, a(n) for n = 0..8192</a>

%F Other identities:

%F a(n) <= A048277(n) for all n.

%F a(n) <= A048967(n) for all n.

%e Row 9 of Pascal's triangle is: {1,9,36,84,126,126,84,36,9,1}. The terms 36 and 84 are only multiples of four, and both of them occur two times on that row, thus a(9) = 2*2 = 4.

%e Row 10 of Pascal's triangle is: {1,10,45,120,210,252,210,120,45,10,1}. The terms 120 (= 4*30) and 252 (= 4*63) are only multiples of four, and the former occurs twice, while the latter is alone at the center, thus a(10) = 2+1 = 3.

%o (PARI)

%o A249732(n) = { my(c=0); for(k=0,n\2,if(!(binomial(n,k)%4),c += (if(k<(n/2),2,1)))); return(c); } \\ Slow...

%o for(n=0, 8192, write("b249732.txt", n, " ", A249732(n)));

%Y Cf. A007318, A034931, A048277, A048645, A072823, A048967, A062296, A187059, A249733.

%K nonn

%O 0,5

%A _Antti Karttunen_, Nov 04 2014

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Last modified February 27 18:02 EST 2020. Contains 332307 sequences. (Running on oeis4.)