login
A026622
a(n) = Sum_{k=0..n} A026615(n, k).
18
1, 2, 5, 12, 26, 54, 110, 222, 446, 894, 1790, 3582, 7166, 14334, 28670, 57342, 114686, 229374, 458750, 917502, 1835006, 3670014, 7340030, 14680062, 29360126, 58720254, 117440510, 234881022, 469762046, 939524094, 1879048190, 3758096382, 7516192766
OFFSET
0,2
COMMENTS
In general, a first order inhomogeneous recurrence of the form s(0) = a, s(n) = m*s(n-1) + k, n>0, will have a closed form of a*m^n +((m^n-1)/(m-1))*k. - Gary Detlefs, Jun 07 2024
FORMULA
a(n) = 7 * 2^(n-2) - 2, a(0) = 1, a(1) = 2 (Cf. A026624). - Ralf Stephan, Feb 05 2004
a(n) = 2*a(n-1) + 2, n>2. - Gary Detlefs, Jun 22 2010
From Colin Barker, Feb 17 2016: (Start)
a(n) = 3*a(n-1) - 2*a(n-2) for n>3.
G.f.: (1 - x + x^2 + x^3)/((1 - x)*(1 - 2*x)). (End)
E.g.f.: (1/4)*( 5 + 2*x - 8*exp(x) + 7*exp(2*x) ). - G. C. Greubel, Jun 24 2024
MATHEMATICA
Table[7*2^(n-2) -2 +Boole[n==1]/2 +(5/4)*Boole[n==0], {n, 0, 40}] (* G. C. Greubel, Jun 24 2024 *)
PROG
(PARI) Vec((1-x+x^2+x^3)/((1-x)*(1-2*x)) + O(x^40)) \\ Colin Barker, Feb 17 2016
(Magma) [n le 1 select n+1 else 7*2^(n-2) -2: n in [0..40]]; // G. C. Greubel, Jun 24 2024
(SageMath) [(7*2^n -8 +2*int(n==1) +5*int(n==0))/4 for n in range(41)] # G. C. Greubel, Jun 24 2024
KEYWORD
nonn,easy
STATUS
approved