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A368346
a(n) = Sum_{k=0..n} 2^(n-k) * floor(k/4).
2
0, 0, 0, 0, 1, 3, 7, 15, 32, 66, 134, 270, 543, 1089, 2181, 4365, 8734, 17472, 34948, 69900, 139805, 279615, 559235, 1118475, 2236956, 4473918, 8947842, 17895690, 35791387, 71582781, 143165569, 286331145, 572662298, 1145324604, 2290649216, 4581298440
OFFSET
0,6
FORMULA
a(n) = a(n-4) + 2^(n-3) - 1.
a(n) = Sum_{k=0..n} floor(2^k/15).
a(n) = 3*a(n-1) - 2*a(n-2) + a(n-4) - 3*a(n-5) + 2*a(n-6).
G.f.: x^4/((1-x) * (1-2*x) * (1-x^4)).
a(n) = floor(2^(n+1)/15) - floor((n+1)/4).
PROG
(PARI) a(n, m=4, k=2) = (k^(n+1)\(k^m-1)-(n+1)\m)/(k-1);
(Python)
def A368346(n): return (1<<n+1)//15-(n+1>>2) # _Chai Wah Wu_, Dec 22 2023
CROSSREFS
Partial sums of A083593.
Sequence in context: A066175 A132978 A336976 * A117079 A026745 A139333
KEYWORD
nonn,easy
AUTHOR
_Seiichi Manyama_, Dec 22 2023
STATUS
approved