This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A298564 #20 Mar 11 2024 01:54:04
%S A298564 0,1,10,53,218,789,2658,8581,26986,83477,255506,776709,2350554,
%T A298564 7092565,21359554,64242437,193054922,579820053,1740770802,5224933765,
%U A298564 15680044090,47050617941,141172825250,423560418693,1270765142058,3812463198229,11437725138898,34313846505221,102942881692826
%N A298564 a(n) = (3^(n+2)+11)/2 - 5*2^(n+1) + 2*n.
%C A298564 Partial sums of A281773; first differences of A285361.
%H A298564 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (7,-17,17,-6)
%F A298564 G.f.: x*(1+3*x) / ( (3*x-1)*(2*x-1)*(x-1)^2 ). - _R. J. Mathar_, Jan 21 2018
%F A298564 a(n) = A249999(n-1) +3*A249999(n-2). - _R. J. Mathar_, Jan 21 2018
%t A298564 Array[(3^(# + 2) + 11)/2 - 5*2^(# + 1) + 2 # &, 29, 0] (* or *)
%t A298564 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 *)
%o A298564 (PARI) A298564(n)=2*n-5<<(n+1)+3^(n+2)\2+5
%o A298564 (Python)
%o A298564 def A298564list(n):
%o A298564 def generator():
%o A298564 a, b, c = 5, 3, 0
%o A298564 while True:
%o A298564 yield c
%o A298564 a *= 2
%o A298564 b *= 3
%o A298564 c += 2 - a + b
%o A298564 a = generator()
%o A298564 return [next(a) for _ in range(n)]
%o A298564 print(A298564list(29)) # _Peter Luschny_, Jan 22 2018
%Y A298564 Cf. A281773, A285361.
%K A298564 nonn,easy
%O A298564 0,3
%A A298564 _M. F. Hasler_, Jan 21 2018