A218394 Numbers such that sum(i<=n) binomial(n,i)*binomial(2*n-2*i, n-i) is not divisible by 5.

1, 5, 7, 11, 25, 27, 31, 35, 37, 51, 55, 57, 61, 125, 127, 131, 135, 137, 151, 155, 157, 161, 175, 177, 181, 185, 187, 251, 255, 257, 261, 275, 277, 281, 285, 287, 301, 305, 307, 311, 625, 627, 631, 635, 637, 651, 655, 657, 661, 675, 677, 681, 685, 687, 751

Offset

1,2

Comments

a(n) = A037453(2*n-1) (proved by Schur, see link).

Links

Table of n, a(n) for n=1..55.

W. Shur, The last digit of C(2*n,n) and Sigma C(n,i)*C(2*n-2*i,n-i), The Electronic Journal of Combinatorics, #R16, Volume 4, Issue 2 (1997).

Formula

a(n) = 2*n - 1 + 2*sum{i=1,n} 5^(i-1)*floor((2*n-1)/3^i).

Prog

(PARI) lista(nb) = {for (n=1, nb, if (sum(i=1, n, binomial(n, i)*binomial(2*n-2*i, n-i)) % 5 != 0, print1(n, ", ")); ); }
(PARI) a(n) = {2*n-1+2*sum(i=1, n, 5^(i-1)*floor((2*n-1)/3^i))}
(Python)
from gmpy2 import digits
def A218394(n): return int(digits((n<<1)-1, 3), 5) # Chai Wah Wu, Aug 10 2025

Crossrefs

Cf. A037453.

Sequence in context: A340308 A339096 A249735 * A067289 A036491 A036490

Adjacent sequences: A218391 A218392 A218393 * A218395 A218396 A218397

Keyword

nonn

Author

Michel Marcus, Oct 28 2012

Status

approved