A026633 a(n) = Sum_{k=0..n} A026626(n, k).

1, 2, 5, 10, 22, 44, 90, 180, 362, 724, 1450, 2900, 5802, 11604, 23210, 46420, 92842, 185684, 371370, 742740, 1485482, 2970964, 5941930, 11883860, 23767722, 47535444, 95070890, 190141780, 380283562, 760567124, 1521134250

Offset: 0

Author

Clark Kimberling

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (2,1,-2).

Crossrefs

Row sums of A026626.

Cf. A026627, A026628, A026629, A026630, A026631, A026632, A026634.

Cf. A026635, A026636, A026961, A026962, A026963, A026964, A026965.

Programs

Magma

[n le 1 select n+1 else (17*2^(n-2) +(-1)^n)/3 -1: n in [0..40]]; // G. C. Greubel, Jun 21 2024

Mathematica

Table[(17*2^(n-2) +(-1)^n)/3 -1 +Boole[n==0]/4 +Boole[n==1]/2, {n, 0, 40}] (* G. C. Greubel, Jun 21 2024 *)

SageMath

[(17*2^(n-2) +(-1)^n)/3 -1 +int(n==0)/4 +int(n==1)/2 for n in range(41)] # G. C. Greubel, Jun 21 2024

Formula

G.f.: (1+x^4)/((1-2*x)*(1-x^2)). - Ralf Stephan, Apr 30 2004

a(n) = (1/3)*(17*2^(n-2) + (-1)^n) - 1, n>=2. - R. J. Mathar, May 22 2013

a(n) = a(n-1) + 2*a(n-2) + 2. - Greg Dresden, Feb 22 2020

E.g.f.: (3 + 6*x - 8*cosh(x) + 17*cosh(2*x) - 16*sinh(x) + 17*sinh(2*x))/12. - Stefano Spezia, Feb 22 2020