A026960 a(n) = Sum_{k=0..n} (k+1) * A026615(n,k).

1, 3, 10, 30, 78, 189, 440, 999, 2230, 4917, 10740, 23283, 50162, 107505, 229360, 487407, 1032174, 2179053, 4587500, 9633771, 20185066, 42205161, 88080360, 183500775, 381681638, 792723429, 1644167140, 3405774819, 7046430690, 14562623457, 30064771040

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 (6,-13,12,-4).

Crossrefs

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

Cf. A026622, A026623, A026624, A026625, A026956, A026957, A026958.

Cf. A026959.

Programs

Magma

[n le 1 select 2*n+1 else 7*(n+2)*2^(n-3) - n - 2: n in [0..40]]; // G. C. Greubel, Jun 16 2024

Mathematica

Join[{1,3},Table[7(n+2)2^(n-3)-n-2,{n,2,30}]] (* or *) LinearRecurrence[ {6,-13,12,-4},{1,3,10,30,78,189},30] (* Harvey P. Dale, Oct 31 2015 *)

PARI

Vec((1-3*x+5*x^2-3*x^3-4*x^4+3*x^5)/((1-x)^2*(1-2*x)^2) + O(x^40)) \\ Colin Barker, Feb 18 2016

SageMath

[7*(n+2)*2^(n-3) - n - 2 + (5/4)*int(n==0) + (3/4)*int(n==1) for n in range(41)] # G. C. Greubel, Jun 16 2024

Formula

For n>1, a(n) = 7*(n+2)*2^(n-3) - n - 2.

From Colin Barker, Feb 18 2016: (Start)

a(n) = 6*a(n-1)-13*a(n-2)+12*a(n-3)-4*a(n-4) for n>5

G.f.: (1-3*x+5*x^2-3*x^3-4*x^4+3*x^5) / ((1-x)^2*(1-2*x)^2).

(End)