A249343 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)).

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

Offset

0,4

Links

Antti Karttunen, Table of n, a(n) for n = 0..6560

Jeffrey C. Lagarias and Harsh Mehta, Products of binomial coefficients and unreduced Farey fractions, arXiv:1409.4145 [math.NT], 2014.

Formula

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

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

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

Prog

(PARI) allocatemem(234567890);
A249343(n) = sum(k=0, n, valuation(binomial(n, k), 3));
for(n=0, 6560, write("b249343.txt", n, " ", A249343(n)));
(Scheme)
(define (A249343 n) (add A243759 (A000217 n) (A000096 n)))
(define (add intfun lowlim uplim) (let sumloop ((i lowlim) (res 0)) (cond ((> i uplim) res) (else (sumloop (+ 1 i) (+ res (intfun i)))))))
(Haskell)
a249343 = a007949 . a001142  -- Reinhard Zumkeller, Mar 16 2015

Crossrefs

Row sums of A243759.

Row 2 of array A249421.

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

Sequence in context: A138002 A261877 A062296 * A369206 A378015 A378014

Adjacent sequences: A249340 A249341 A249342 * A249344 A249345 A249346

Keyword

nonn

Author

Antti Karttunen, Oct 28 2014

Status

approved