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The exponent of the highest power of 3 dividing the product of the elements on the n-th row of Pascal's triangle (A001142(n)).
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%I #22 Jul 22 2022 10:47:16

%S 0,0,0,2,1,0,4,2,0,14,10,6,13,8,3,12,6,0,28,20,12,24,15,6,20,10,0,68,

%T 55,42,58,44,30,48,33,18,73,56,39,60,42,24,47,28,9,78,57,36,62,40,18,

%U 46,23,0,136,110,84,114,87,60,92,64,36,132,102,72,107,76,45,82,50,18,128,94,60,100,65,30,72,36,0

%N The exponent of the highest power of 3 dividing the product of the elements on the n-th row of Pascal's triangle (A001142(n)).

%H Antti Karttunen, <a href="/A249343/b249343.txt">Table of n, a(n) for n = 0..6560</a>

%H Jeffrey C. Lagarias and Harsh Mehta, <a href="http://arxiv.org/abs/1409.4145">Products of binomial coefficients and unreduced Farey fractions</a>, arXiv:1409.4145 [math.NT], 2014.

%F a(n) = A007949(A001142(n)).

%F a(n) = Sum_{k=0..n} A243759(n,k).

%F a(n) = Sum_{i=1..n} (2*i-n-1)*v_3(i), where v_3(i) = A007949(i) is the exponent of the highest power of 3 dividing i. - _Ridouane Oudra_, Jun 02 2022

%o (PARI) allocatemem(234567890);

%o A249343(n) = sum(k=0, n, valuation(binomial(n, k), 3));

%o for(n=0, 6560, write("b249343.txt", n, " ", A249343(n)));

%o (Scheme)

%o (define (A249343 n) (add A243759 (A000217 n) (A000096 n)))

%o (define (add intfun lowlim uplim) (let sumloop ((i lowlim) (res 0)) (cond ((> i uplim) res) (else (sumloop (+ 1 i) (+ res (intfun i)))))))

%o (Haskell)

%o a249343 = a007949 . a001142 -- _Reinhard Zumkeller_, Mar 16 2015

%Y Row sums of A243759.

%Y Row 2 of array A249421.

%Y Cf. A001142, A007949, A187059, A249345, A249347.

%K nonn

%O 0,4

%A _Antti Karttunen_, Oct 28 2014