A365103 Number of distinct quartic residues x^4 (mod 4^n), x=0..4^n-1.
1, 2, 2, 6, 18, 70, 274, 1094, 4370, 17478, 69906, 279622, 1118482, 4473926, 17895698, 71582790, 286331154, 1145324614, 4581298450, 18325193798, 73300775186, 293203100742, 1172812402962, 4691249611846, 18764998447378
Offset: 0
Keywords
Links
- Index entries for linear recurrences with constant coefficients, signature (4, 1, -4).
Programs
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Mathematica
a[n_] = Ceiling[4^n/15] + Boole[Mod[n,2]==1]; Array[a, 24]
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PARI
a(n) = ceil(4^n/15)+(Mod(n,2)==1);
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Python
def A365103(n): return len({pow(x,4,1<<(n<<1)) for x in range(1<<(n<<1))}) # Chai Wah Wu, Sep 18 2023
Formula
a(n) = ceiling(4^n/15) + (n mod 2).
Comments