A060188 A column and diagonal of A060187.

1, 6, 23, 76, 237, 722, 2179, 6552, 19673, 59038, 177135, 531428, 1594309, 4782954, 14348891, 43046704, 129140145, 387420470, 1162261447, 3486784380, 10460353181, 31381059586, 94143178803, 282429536456, 847288609417

Offset

2,2

Comments

Sums of rows of the numerators and of the denominators of the redundant Stern-Brocot structure A152975/A152976: a(n+2) = Sum_{k=2^n..(2^(n+1) -1)} A152975(k) = Sum_{k=2^n..(2^(n+1) -1)} A152976(k). - Reinhard Zumkeller, Dec 22 2008

Links

Vincenzo Librandi, Table of n, a(n) for n = 2..2000

P. A. MacMahon, The divisors of numbers, Proc. London Math. Soc., (2) 19 (1920), 305-340; Coll. Papers II, pp. 267-302.

Index entries for linear recurrences with constant coefficients, signature (5,-7,3).

Formula

a(n) = 3^(n-1) - n = A061980(n-1, 2). - Henry Bottomley, May 24 2001

From Paul Barry, Jun 24 2003: (Start)

With offset 0, this is 3^(n+1) - n - 2.

Partial sums of A048473. (End)

From Colin Barker, Dec 19 2012: (Start)

a(n) = 5*a(n-1) - 7*a(n-2) + 3*a(n-3).

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

E.g.f.: (exp(3*x) - 3*x*exp(x) - 1)/3. - Wolfdieter Lang, Apr 17 2017

Maple

a[0]:=1:for n from 1 to 24 do a[n]:=(4*a[n-1]-3*a[n-2]+2) od: seq(a[n], n=0..24); # Zerinvary Lajos, Jun 08 2007

Mathematica

Table[3^(n-1) -n, {n, 2, 30}] (* Vladimir Joseph Stephan Orlovsky, Nov 15 2008 *)

Prog

(Magma) [3^(n-1)-n: n in [2..30]]; // Vincenzo Librandi, Sep 05 2011
(Sage) [3^(n-1) -n for n in (2..32)] # G. C. Greubel, Jan 07 2022

Crossrefs

Cf. A048473, A060187 (first differences).

Sequence in context: A136530 A259033 A054459 * A058751 A034359 A220148

Adjacent sequences: A060185 A060186 A060187 * A060189 A060190 A060191

Keyword

nonn,easy

Author

N. J. A. Sloane, Mar 20 2001

Extensions

More terms from Vladeta Jovovic, Mar 20 2001

Status

approved