login
This site is supported by donations to The OEIS Foundation.

 

Logo

Thanks to everyone who made a donation during our annual appeal!
To see the list of donors, or make a donation, see the OEIS Foundation home page.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A194459 Number of entries in the n-th 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 (list; graph; refs; listen; history; text; internal format)
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] (* Jean-Fran├žois 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified January 18 16:40 EST 2019. Contains 319271 sequences. (Running on oeis4.)