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%I M3510 #27 Feb 19 2024 11:49:56
%S 1,4,16,40,136,304,880,1768,4936,9112,25216,45016,121600,212944,
%T 571552,982240,2616136,4456384,11785408,19922872,52402336,88076560,
%U 230641504,385875880,1006499200,1677720304,4361862976,7247738776,18789905872,31138512784,80529599680,133143986056,343594756936
%N Let S denote the palindromes in the language {0,1,2,3}*; a(n) = number of words of length n in the language SS.
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H R. Kemp, <a href="http://dx.doi.org/10.1016/0012-365X(82)90123-6">On the number of words in the language {w in Sigma* | w = w^R }^2</a>, Discrete Math., 40 (1982), 225-234.
%F a(n) = A187274(n) - Sum_{d|n,d<n} phi(n/d)*a(d). - _Sean A. Irvine_, Sep 27 2017
%p See A007055.
%o (Python)
%o from functools import lru_cache
%o from sympy import totient, proper_divisors
%o @lru_cache(maxsize=None)
%o def A007057(n): return (n<<n+1 if n&1 else 5*(n>>1)<<n)-sum(totient(n//d)*A007057(d) for d in proper_divisors(n,generator=True)) if n else 1 # _Chai Wah Wu_, Feb 19 2024
%Y Column 4 of A284873.
%K nonn
%O 0,2
%A _N. J. A. Sloane_, _Mira Bernstein_, R. Kemp
%E Entry revised by _N. J. A. Sloane_, Mar 07 2011
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