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

Author

N. J. A. Sloane, Mar 20 2001

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A048473, A060187 (first differences).

Programs

Magma

[3^(n-1)-n: n in [2..30]]; // Vincenzo Librandi, Sep 05 2011

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 *)
LinearRecurrence[{5,-7,3},{1,6,23},30] (* Harvey P. Dale, Jul 03 2024 *)

Sage

[3^(n-1) -n for n in (2..32)] # G. C. Greubel, Jan 07 2022

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

Extensions

More terms from Vladeta Jovovic, Mar 20 2001