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A194459
Number of entries in the n-th row of Pascal's triangle not divisible by 5.
5
1, 2, 3, 4, 5, 2, 4, 6, 8, 10, 3, 6, 9, 12, 15, 4, 8, 12, 16, 20, 5, 10, 15, 20, 25, 2, 4, 6, 8, 10, 4, 8, 12, 16, 20, 6, 12, 18, 24, 30, 8, 16, 24, 32, 40, 10, 20, 30, 40, 50, 3, 6, 9, 12, 15, 6, 12, 18, 24, 30, 9, 18, 27, 36, 45, 12, 24, 36, 48, 60, 15, 30
OFFSET
0,2
COMMENTS
Pascal triangles modulo p with p prime have the dimension D = log(p*(p+1)/2)/log(p). [Corrected by Connor Lane, Nov 28 2022]
Also number of ones in row n of triangle A254609. - Reinhard Zumkeller, Feb 04 2015
LINKS
FORMULA
a(n) = Product_{d=1..4} (d+1)^b(n,d) with b(n,d) = number of digits d in base 5 expansion of n. The formula generalizes to other prime bases p.
a(n) = A194458(n) - A194458(n-1).
EXAMPLE
n = 32 = 112|_5: b(32,1) = 2, b(32,2) = 1, thus a(32) = 2^2 * 3^1 = 12.
MAPLE
a:= proc(n) local l, m, t;
m:= n;
l:= [0$5];
while m>0 do t:= irem(m, 5, 'm')+1; l[t]:=l[t]+1 od;
mul(r^l[r], r=2..5)
end:
seq(a(n), n=0..100);
MATHEMATICA
Nest[Join[#, 2#, 3#, 4#, 5#]&, {1}, 4] (* Jean-François Alcover, Apr 12 2017, after code by Robert G. Wilson v in A006047 *)
PROG
(Haskell)
a194459 = sum . map (signum . flip mod 5) . a007318_row
-- Reinhard Zumkeller, Feb 04 2015
CROSSREFS
Cf. A006046, A001316 (for p=2).
Cf. A006048, A006047 (for p=3).
Cf. A194458 (for p=5).
Sequence in context: A141809 A309435 A043265 * A143120 A353277 A308201
KEYWORD
nonn,look
AUTHOR
Paul Weisenhorn, Aug 24 2011
EXTENSIONS
Edited by Alois P. Heinz, Sep 06 2011
STATUS
approved