

A194459


Number of entries in the nth 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
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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]


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.


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



PROG

(Haskell)
a194459 = sum . map (signum . flip mod 5) . a007318_row


CROSSREFS



KEYWORD



AUTHOR



EXTENSIONS



STATUS

approved



