A101693 A modular binomial sum transform of 2^n.

1, 1, 5, 1, 21, 1, 5, 17, 341, 1, 5, 17, 85, 257, 1285, 4369, 87381, 1, 5, 17, 85, 257, 1285, 4369, 21845, 65537, 327685, 1114129, 5570645, 16843009, 84215045, 286331153, 5726623061, 1, 5, 17, 85, 257, 1285, 4369, 21845, 65537, 327685, 1114129, 5570645

Offset

0,3

Comments

b(2^n+1) is 5,1,1,1,....

Links

Table of n, a(n) for n=0..44.

Formula

a(n) = Sum_{k=0..n} mod(binomial(2n-2, k), 2)*2^k.

a(2^n) = A101694(n);

Mathematica

Table[Sum[Mod[Binomial[2n-2, k], 2]2^k, {k, 0, n}], {n, 0, 50}] (* Harvey P. Dale, Nov 23 2019 *)

Prog

(Python)
def A101693(n): return sum((not ~(n-1<<1)&k)<<k for k in range(n+1)) # Chai Wah Wu, Jul 31 2025

Crossrefs

Cf. A001045, A101694.

Sequence in context: A070729 A348501 A296306 * A063476 A126325 A278544

Adjacent sequences: A101690 A101691 A101692 * A101694 A101695 A101696

Keyword

easy,nonn

Author

Paul Barry, Dec 11 2004

Status

approved