A101623 Modular binomial transform of 10^n.
1, 1, 11, 1, 111, 101, 1011, 1, 10111, 10101, 111011, 10001, 1100111, 1000101, 10001011, 1, 100010111, 100010101, 1100111011, 100010001, 11101100111, 10101000101, 101110001011, 100000001, 1011000010111, 1010000010101, 11100000111011, 1000000010001, 110000001100111
Offset: 0
Crossrefs
A101624 in binary.
Programs
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PARI
a(n) = sum(k=0, n, lift(Mod(binomial(k, n-k), 2))*10^(n-k)); \\ Michel Marcus, Jul 31 2025
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Python
def A101623(n): return sum(int(not k & ~(n-k))*10**k for k in range((n>>1)+1)) # Chai Wah Wu, Jul 30 2025
Formula
a(n) = Sum_{k=0..floor(n/2)} mod(binomial(n-k, k), 2)*10^k.
a(n) = Sum_{k=0..n} mod(binomial(k, n-k), 2)*10^(n-k).
Extensions
More terms from Michel Marcus, Jul 31 2025