A298564 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,3

COMMENTS

Partial sums of A281773; first differences of A285361.

LINKS

Table of n, a(n) for n=0..28.

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

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

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 *)

PROG

(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

CROSSREFS

Cf. A281773, A285361.

Sequence in context: A119543 A302302 A216938 * A063899 A006889 A300422

Adjacent sequences: A298561 A298562 A298563 * A298565 A298566 A298567

KEYWORD

nonn,easy

AUTHOR

M. F. Hasler, Jan 21 2018

STATUS

approved