A101945 a(n) = 6*2^n - n - 5.

1, 6, 17, 40, 87, 182, 373, 756, 1523, 3058, 6129, 12272, 24559, 49134, 98285, 196588, 393195, 786410, 1572841, 3145704, 6291431, 12582886, 25165797, 50331620, 100663267, 201326562, 402653153, 805306336, 1610612703, 3221225438

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (4,-5,2).

Formula

a(n) = 4*a(n-1) - 5*a(n-2) + 2*a(n-3) for n >= 3.

Row sums of triangle A135855. - Gary W. Adamson, Dec 01 2007

From G. C. Greubel, Feb 06 2022: (Start)

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

E.g.f.: 6*exp(2*x) - (5+x)*exp(x). (End)

Mathematica

a[0]=1; a[1]=6; a[2]=17; a[n_]:= a[n]= 4a[n-1] -5a[n-2] +2a[n-3];
Table[a[n], {n, 0, 30}] (* Robert G. Wilson v, Jan 12 2005 *)

Prog

(PARI) a(n)=if(n==1, 1, if(n==2, 6, if(n==3, 17, 4*a(n-1)-5*a(n-2)+2*a(n-3)))) \\ (Klasen)
(Magma) [6*2^n -n-5: n in [0..40]]; // G. C. Greubel, Feb 06 2022
(Sage) [3*2^(n+1) -(n+5) for n in (0..40)] # G. C. Greubel, Feb 06 2022

Crossrefs

Cf. A033484, A101946, A135855.

Sequence in context: A080275 A061349 A213780 * A220407 A013319 A047861

Adjacent sequences: A101942 A101943 A101944 * A101946 A101947 A101948

Keyword

nonn,easy

Author

Gary W. Adamson, Dec 22 2004

Extensions

More terms from Lambert Klasen (Lambert.Klasen(AT)gmx.net), Jan 06 2005

New definition from Ralf Stephan, May 17 2007

Status

approved