A026635 a(n) = Sum_{i=0..n} Sum_{j=0..n} A026626(i,j).

1, 3, 8, 18, 40, 84, 174, 354, 716, 1440, 2890, 5790, 11592, 23196, 46406, 92826, 185668, 371352, 742722, 1485462, 2970944, 5941908, 11883838, 23767698, 47535420, 95070864, 190141754, 380283534, 760567096, 1521134220, 3042268470, 6084536970, 12169073972

Offset: 0

Author

Clark Kimberling

Keywords

• nonn
• easy

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (3,-1,-3,2).

Crossrefs

Cf. A026626, A026627, A026628, A026629, A026630, A026631, A026632.

Cf. A026633, A026634, A026636, A026961, A026962, A026963, A026964.

Cf. A026965.

Programs

Magma

[n eq 0 select 1 else (17*2^n -6*n-9+(-1)^n)/6: n in [0..40]]; // G. C. Greubel, Jun 21 2024

Mathematica

LinearRecurrence[{3,-1,-3,2},{1,3,8,18,40},40] (* Harvey P. Dale, Jan 17 2024 *)

PARI

Vec((1 + x^4) / ((1 - x)^2*(1 + x)*(1 - 2*x)) + O(x^40)) \\ Colin Barker, Sep 29 2017

SageMath

[(17*2^n -6*n -9 +(-1)^n -3*int(n==0))/6 for n in range(41)] # G. C. Greubel, Jun 21 2024

Formula

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

From Colin Barker, Sep 29 2017: (Start)

a(n) = (17*2^n - 6*n - 9 + (-1)^n)/6 for n>0.

a(n) = 3*a(n-1) - a(n-2) - 3*a(n-3) + 2*a(n-4) for n>4. (End)

E.g.f.: (1/6)*(-3 - 3*(3+2*x)*exp(x) + 17*exp(2*x) + exp(-x)). - G. C. Greubel, Jun 21 2024