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 *)
LinearRecurrence[{5, -7, 3}, {1, 6, 23}, 30] (* Harvey P. Dale, Jul 03 2024 *)
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
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Mar 20 2001
EXTENSIONS
More terms from Vladeta Jovovic, Mar 20 2001
STATUS
approved