A298564 a(n) = (3^(n+2)+11)/2 - 5*2^(n+1) + 2*n.

0, 1, 10, 53, 218, 789, 2658, 8581, 26986, 83477, 255506, 776709, 2350554, 7092565, 21359554, 64242437, 193054922, 579820053, 1740770802, 5224933765, 15680044090, 47050617941, 141172825250, 423560418693, 1270765142058, 3812463198229, 11437725138898, 34313846505221, 102942881692826

Offset: 0

Author

M. F. Hasler, Jan 21 2018

Keywords

• nonn
• easy

Comments

Partial sums of A281773; first differences of A285361.

Links

• Index entries for linear recurrences with constant coefficients, signature (7,-17,17,-6)

Crossrefs

Cf. A281773, A285361.

Programs

Mathematica

Array[(3^(# + 2) + 11)/2 - 5*2^(# + 1) + 2 # &, 29, 0] (* or *)
CoefficientList[Series[x (1 + 3 x)/((3 x - 1) (2 x - 1) (x - 1)^2), {x, 0, 28}], x] (* Michael De Vlieger, Jan 21 2018 *)

PARI

A298564(n)=2*n-5<<(n+1)+3^(n+2)\2+5

Python

def A298564list(n):
    def generator():
        a, b, c = 5, 3, 0
        while True:
            yield c
            a *= 2
            b *= 3
            c += 2 - a + b
    a = generator()
    return [next(a) for _ in range(n)]
print(A298564list(29)) # Peter Luschny, Jan 22 2018

Formula

G.f.: x*(1+3*x) / ( (3*x-1)*(2*x-1)*(x-1)^2 ). - R. J. Mathar, Jan 21 2018

a(n) = A249999(n-1) +3*A249999(n-2). - R. J. Mathar, Jan 21 2018