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A062296
a(n) = number of entries in n-th row of Pascal's triangle divisible by 3.
10
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, 24, 27, 24, 21, 28, 23, 18, 33, 30, 27, 32, 25, 18, 31, 20, 9, 40, 35, 30, 37, 26, 15, 34, 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
OFFSET
0,4
COMMENTS
a(n) = n + 1 - A206424(n) - A227428(n); number of zeros in row n of triangle A083093. - Reinhard Zumkeller, Jul 11 2013
LINKS
FORMULA
a(n) + A006047(n) = n + 1 so a(n) = n + 1 - A006047(n).
EXAMPLE
When n=3 the row is 1,3,3,1 so a(3) = 2.
MAPLE
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
MATHEMATICA
a[n_] := Count[(Binomial[n, #] & )[Range[0, n]], _?(Divisible[#, 3] & )];
Table[a[n], {n, 0, 100}] (* Jean-François Alcover, Jan 26 2018 *)
PROG
(Haskell)
a062296 = sum . map ((1 -) . signum) . a083093_row
-- Reinhard Zumkeller, Jul 11 2013
CROSSREFS
Cf. A006047.
Sequence in context: A348218 A138002 A261877 * A249343 A369206 A378015
KEYWORD
nonn,look
AUTHOR
Ahmed Fares (ahmedfares(AT)my-deja.com), Jul 02 2001
EXTENSIONS
More terms from Emeric Deutsch, Feb 03 2005
STATUS
approved