A368345 a(n) = Sum_{k=0..n} 4^(n-k) * floor(k/3).

0, 0, 0, 1, 5, 21, 86, 346, 1386, 5547, 22191, 88767, 355072, 1420292, 5681172, 22724693, 90898777, 363595113, 1454380458, 5817521838, 23270087358, 93080349439, 372321397763, 1489285591059, 5957142364244, 23828569456984, 95314277827944, 381257111311785

Offset

0,5

Links

Table of n, a(n) for n=0..27.

Index entries for linear recurrences with constant coefficients, signature (5,-4,1,-5,4).

Formula

a(n) = a(n-3) + (4^(n-2) - 1)/3.

a(n) = 1/3 * Sum_{k=0..n} floor(4^k/21) = Sum_{k=0..n} floor(4^k/63).

a(n) = 5*a(n-1) - 4*a(n-2) + a(n-3) - 5*a(n-4) + 4*a(n-5).

G.f.: x^3/((1-x) * (1-4*x) * (1-x^3)).

a(n) = (floor(4^(n+1)/63) - floor((n+1)/3))/3.

Prog

(PARI) a(n, m=3, k=4) = (k^(n+1)\(k^m-1)-(n+1)\m)/(k-1);

Crossrefs

Partial sums of A033140.

Column k=4 of A368343.

Cf. A097138.

Sequence in context: A272832 A273489 A097113 * A265939 A012814 A039919

Adjacent sequences: A368342 A368343 A368344 * A368346 A368347 A368348

Keyword

nonn,easy

Author

Seiichi Manyama, Dec 22 2023

Status

approved