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A007058
Let S denote the palindromes in the language {0,1,2,3,4}*; a(n) = number of words of length n in the language SS.
(Formerly M3936)
4
1, 5, 25, 65, 265, 605, 2125, 4345, 14665, 27965, 93025, 171825, 559645, 1015565, 3276725, 5857865, 18734665, 33203045, 105436225, 185546785, 585842065, 1025381485, 3222484125, 5615234265, 17577530845, 30517575605, 95213827825, 164794865465, 512692025285, 885009765485, 2746575977125
OFFSET
0,2
REFERENCES
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
FORMULA
a(n) = A187275(n) - Sum_{d|n,d<n} phi(n/d)*a(d). - Sean A. Irvine, Sep 27 2017
MAPLE
See A007055.
PROG
(Python)
from functools import lru_cache
from sympy import totient, proper_divisors
@lru_cache(maxsize=None)
def A007058(n): return (n*5**(1+(n>>1)) if n&1 else 3*n*5**(n>>1))-sum(totient(n//d)*A007058(d) for d in proper_divisors(n, generator=True)) if n else 1 # Chai Wah Wu, Feb 19 2024
CROSSREFS
Column 5 of A284873.
Sequence in context: A179131 A054994 A108403 * A071383 A088959 A018782
KEYWORD
nonn
AUTHOR
EXTENSIONS
Entry revised by N. J. A. Sloane, Mar 07 2011
STATUS
approved