

A194459


Number of entries in the nth row of Pascal's triangle not divisible by 5.


4



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

All Pascal triangles modulo p with p prime have the dimension D=log(3)/log(2).
Also number of ones in row n of triangle A254609.  Reinhard Zumkeller, Feb 04 2015


LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..10000


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

Nest[Join[#, 2#, 3#, 4#, 5#]&, {1}, 4] (* JeanFrançois 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

A006046(n+1) = A006046(n)+A001316(n) for p=2.
A006048(n+1) = A006048(n)+A006047(n+1) for p=3.
A194458(n+1) = A194458(n)+A194459(n+1) for p=5.
Cf. A007318, A254609.
Sequence in context: A141810 A141809 A043265 * A143120 A026362 A223490
Adjacent sequences: A194456 A194457 A194458 * A194460 A194461 A194462


KEYWORD

nonn,look


AUTHOR

Paul Weisenhorn, Aug 24 2011


EXTENSIONS

Edited by Alois P. Heinz, Sep 06 2011


STATUS

approved



