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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 (list; graph; refs; listen; history; text; internal format)
 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 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. 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). Cf. A007318, A254609. Sequence in context: A141809 A309435 A043265 * A143120 A353277 A308201 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

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Last modified December 1 22:24 EST 2023. Contains 367502 sequences. (Running on oeis4.)