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A367484
Number of integers of the form (x^4 + y^4) mod 3^n; a(n) = A289559(3^n).
1
1, 3, 7, 19, 55, 165, 493, 1477, 4429, 13287, 39859, 119575, 358723, 1076169, 3228505, 9685513, 29056537
OFFSET
0,2
COMMENTS
It appears that for n > 4: a(n) = 2*3^(n-1) + a(n-4).
For n < 5: a(n) = 2*3^(n-1) + 1.
Conjecture in closed form: a(n) = 2*ceiling(3^(n+3)/80) - 1.
FORMULA
Conjecture: a(n) = 2*ceiling(3^(n+3)/80) - 1.
a(n) = A289559(3^n). - Thomas Scheuerle, Nov 20 2023
PROG
(PARI) a(n) = #setbinop((x, y)->Mod(x, 3^n)^4+Mod(y, 3^n)^4, [0..3^n-1]);
(Python)
def A367484(n):
m = 3**n
return len({(pow(x, 4, m)+pow(y, 4, m))%m for x in range(m) for y in range(x+1)}) # Chai Wah Wu, Jan 23 2024
CROSSREFS
Subsequence of A289559.
Sequence in context: A183115 A183120 A100702 * A224031 A147586 A305197
KEYWORD
nonn,more
AUTHOR
Albert Mukovskiy, Nov 19 2023
STATUS
approved