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A185376 Number of binary necklaces of 2n beads for which a cut exists producing a palindrome. 2
2, 3, 6, 9, 20, 34, 72, 129, 272, 516, 1056, 2050, 4160, 8200, 16512, 32769, 65792, 131088, 262656, 524292, 1049600, 2097184, 4196352, 8388610, 16781312, 33554496, 67117056, 134217736, 268451840, 536871040, 1073774592, 2147483649 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

These are the values of A185333 for even n.

Conjecture: a(n) = 2^(n-1) + 2^((n-2^t)/(2^(t+1))), where t = number of factors of 2 in n.

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..1000

FORMULA

a(n) = A185333(2n).

MATHEMATICA

f[n_] := Block[{k = IntegerExponent[n, 2]}, 2^n/2 + 2^((n - 2^k)/(2^(k + 1)))]; Array[f, 32] (* Robert G. Wilson v, Aug 08 2011 *)

PROG

(Python)

def a185333(n):

    if n%2==1: return 2**((n + 1)/2)

    k=bin(n - 1)[2:].count('1') - bin(n)[2:].count('1')

    return 2**(n/2 - 1) + 2**((n/2 - 2**k)/(2**(k + 1)))

def a(n): return a185333(2*n)

print [a(n) for n in range(1, 101)] # Indranil Ghosh, Jun 29 2017, after the formula

CROSSREFS

Cf. A185333.

Sequence in context: A246565 A320169 A293606 * A321484 A191469 A091053

Adjacent sequences:  A185373 A185374 A185375 * A185377 A185378 A185379

KEYWORD

nonn

AUTHOR

Tony Bartoletti, Feb 20 2011

STATUS

approved

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Last modified June 4 17:14 EDT 2020. Contains 334828 sequences. (Running on oeis4.)