A026622 a(n) = Sum_{k=0..n} A026615(n, k).

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

Author

Clark Kimberling

Keywords

• nonn
• easy

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

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (3,-2).

Crossrefs

Cf. A026615, A026616, A026617, A026618, A026619, A026620, A026621.

Cf. A026623, A026624, A026625, A026956, A026957, A026958, A026959.

Cf. A026960.

Programs

Magma

[n le 1 select n+1 else 7*2^(n-2) -2: n in [0..40]]; // 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 *)

PARI

Vec((1-x+x^2+x^3)/((1-x)*(1-2*x)) + O(x^40)) \\ Colin Barker, Feb 17 2016

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

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