OFFSET
1,2
COMMENTS
Cf. property described by Gary Detlefs in A113801: more generally, these numbers are of the form (2*h*n+(h-4)*(-1)^n-h)/4 (h, n natural numbers), therefore ((2*h*n+(h-4)*(-1)^n-h)/4)^2-1 == 0 (mod h); in this case, a(n)^2-1 == 0 (mod 7). - Bruno Berselli, Nov 17 2010
LINKS
Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
Index entries for linear recurrences with constant coefficients, signature (1,1,-1).
FORMULA
a(1) = 1; a(n) = 7(n-1) - a(n-1). - Rolf Pleisch, Jan 31 2008 (corrected by Jon E. Schoenfield, Dec 22 2008)
a(n) = (7/2)*(n-(1-(-1)^n)/2) - (-1)^n. - Rolf Pleisch, Nov 02 2010
From Bruno Berselli, Nov 17 2010: (Start)
G.f.: x*(1+5*x+x^2)/((1+x)*(1-x)^2).
a(n) = -a(-n+1) = a(n-1) + a(n-2) - a(n-3).
a(n) = a(n-2)+7.
a(n) = 7*A000217(n-1)+1 - 2*Sum_{i=1..n-1} a(i) for n > 1. (End)
a(n) = 7*floor(n/2)+(-1)^(n+1). - Gary Detlefs, Dec 29 2011
E.g.f.: 1 + ((14*x - 7)*exp(x) + 3*exp(-x))/4. - David Lovler, Sep 01 2022
From Amiram Eldar, Nov 22 2024: (Start)
Product_{n>=1} (1 - (-1)^n/a(n)) = 2*cos(Pi/7) (A160389).
Product_{n>=2} (1 + (-1)^n/a(n)) = (Pi/7) * cosec(Pi/7) (A371858). (End)
MATHEMATICA
Rest[Flatten[Table[{7i-1, 7i+1}, {i, 0, 40}]]] (* Harvey P. Dale, Nov 20 2010 *)
PROG
(Magma) [n: n in [1..210]| n mod 7 in {1, 6}]; // Bruno Berselli, Feb 22 2011
(Haskell)
a047336 n = a047336_list !! (n-1)
a047336_list = 1 : 6 : map (+ 7) a047336_list
-- Reinhard Zumkeller, Jan 07 2012
(PARI) a(n)=n\2*7-(-1)^n \\ Charles R Greathouse IV, May 02 2016
CROSSREFS
KEYWORD
nonn,easy,changed
AUTHOR
EXTENSIONS
More terms from Jon E. Schoenfield, Jan 18 2009
STATUS
approved