A185376 Number of binary necklaces of 2n beads for which a cut exists producing a palindrome.
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
Offset: 1
Keywords
Links
- G. C. Greubel, Table of n, a(n) for n = 1..1000
Crossrefs
Cf. A185333.
Programs
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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 *) -
Python
def a185333(n): if n%2: 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
Formula
a(n) = A185333(2n).
Comments