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a(n) = number of entries in n-th row of Pascal's triangle divisible by 3.
10

%I #14 Jan 26 2018 05:08:48

%S 0,0,0,2,1,0,4,2,0,8,7,6,9,6,3,10,5,0,16,14,12,16,11,6,16,8,0,26,25,

%T 24,27,24,21,28,23,18,33,30,27,32,25,18,31,20,9,40,35,30,37,26,15,34,

%U 17,0,52,50,48,52,47,42,52,44,36,58,53,48,55,44,33,52,35,18,64,56,48,58,41

%N a(n) = number of entries in n-th row of Pascal's triangle divisible by 3.

%C a(n) = n + 1 - A206424(n) - A227428(n); number of zeros in row n of triangle A083093. - _Reinhard Zumkeller_, Jul 11 2013

%H Reinhard Zumkeller, <a href="/A062296/b062296.txt">Table of n, a(n) for n = 0..1000</a>

%F a(n) + A006047(n) = n + 1 so a(n) = n + 1 - A006047(n).

%e When n=3 the row is 1,3,3,1 so a(3) = 2.

%p p:=proc(n) local ct, k: ct:=0: for k from 0 to n do if binomial(n,k) mod 3 = 0 then else ct:=ct+1 fi od: end: seq(n+1-p(n),n=0..83); # _Emeric Deutsch_

%t a[n_] := Count[(Binomial[n, #] & )[Range[0, n]], _?(Divisible[#, 3] & )];

%t Table[a[n], {n, 0, 100}] (* _Jean-François Alcover_, Jan 26 2018 *)

%o (Haskell)

%o a062296 = sum . map ((1 -) . signum) . a083093_row

%o -- _Reinhard Zumkeller_, Jul 11 2013

%Y Cf. A006047.

%K nonn,look

%O 0,4

%A Ahmed Fares (ahmedfares(AT)my-deja.com), Jul 02 2001

%E More terms from _Emeric Deutsch_, Feb 03 2005

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Last modified September 19 21:59 EDT 2024. Contains 376015 sequences. (Running on oeis4.)