A368346 a(n) = Sum_{k=0..n} 2^(n-k) * floor(k/4).

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

Author

Seiichi Manyama, Dec 22 2023

Keywords

• nonn
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (3,-2,0,1,-3,2).

Crossrefs

Partial sums of A083593.

Cf. A178420, A178452, A178455, A178457, A178459, A178460, A178742.

Programs

PARI

a(n, m=4, k=2) = (k^(n+1)\(k^m-1)-(n+1)\m)/(k-1);

Python

def A368346(n): return (1<>2) # Chai Wah Wu, Dec 22 2023

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).