A208279 Central terms of Pascal's triangle mod 10 (A008975).

1, 2, 6, 0, 0, 2, 4, 2, 0, 0, 6, 2, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 4, 2, 0, 0, 4, 8, 4, 0, 0, 2, 4, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 2, 6, 0, 0, 2, 4, 2, 0, 0, 6, 2, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0

Offset

0,2

Comments

From Chai Wah Wu, Dec 08 2023: (Start)

Last digit of central binomial coefficient binomial(2n,n) in base 10.

A000984 mod 10.

A073095 are numbers n such that a(n) = A008904(n).

a(n) is even for n>0. (End)

From Robert Israel, Dec 08 2023: (Start)

If at least one base-5 digit of n is 3 or 4, then a(n) = 0.

Otherwise, if k 1's occur in the base-5 expansion of n, then a(n) = 2^k (mod 10) if k > 0, or 6 if k = 0. (End)

Links

Reinhard Zumkeller, Table of n, a(n) for n = 0..1000

Formula

a(n) = A008975(2*n,n) = binomial(2n,n) mod 10.

Maple

f:= proc(n) local A, v;
   A:= convert(n, base, 5);
   if select(`>=`, A, 3) <> [] then return 0 fi;
   v:= numboccur(1, A);
   if v > 0 then 2^v mod 10
   else 6
   fi
end proc:
f(0):= 1:
map(f, [$0..200]); # Robert Israel, Dec 08 2023

Mathematica

Array[Mod[Binomial[2#, #], 10]&, 100, 0] (* Paolo Xausa, Dec 09 2023 *)

Prog

(Haskell)
a208279 n = a008975 (2*n) n
(Python)
from sympy.ntheory.factor_ import digits
def A208279(n):
    if n == 0: return 1
    s = digits(n, 5)[1:]
    return 0 if any(x>2 for x in s) else ((6, 2, 4, 8)[a&3] if (a:=s.count(1)) else 6) # Chai Wah Wu, Dec 08 2023

Crossrefs

Cf. A000984, A008904, A008975, A073095.

Sequence in context: A340984 A122760 A358029 * A186502 A165733 A330327

Adjacent sequences: A208276 A208277 A208278 * A208280 A208281 A208282

Keyword

nonn,base

Author

Reinhard Zumkeller, Feb 25 2012

Status

approved