OFFSET
1,2
COMMENTS
The terms are the negatives of A141354 and therefore have the same generating function except the sign.
LINKS
Colin Barker, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (2,0,-2,1).
FORMULA
a(n) = n^2 - 2^(n mod 2) = -A141354(n-1).
From Colin Barker, Jun 27 2015: (Start)
a(n) = n^2 - 1 for n even; a(n) = n^2 - 2 for n odd.
a(n) = 2*a(n-1) - 2*a(n-3) + a(n-4).
G.f.: x*(x^3-x^2-5*x+1) / ((x-1)^3*(x+1)).
(End)
MATHEMATICA
Table[n^2-2^Mod[n, 2], {n, 50}] (* Ray Chandler, Dec 05 2011*)
LinearRecurrence[{2, 0, -2, 1}, {-1, 3, 7, 15}, 50] (* Harvey P. Dale, Nov 16 2019 *)
PROG
(PARI) Vec(x*(x^3-x^2-5*x+1)/((x-1)^3*(x+1)) + O(x^100)) \\ Colin Barker, Jun 27 2015
CROSSREFS
KEYWORD
easy,sign
AUTHOR
Jerzy Kocik (jkocik(AT)siu.edu), Oct 03 2010
EXTENSIONS
Edited by Ray Chandler, Dec 05 2011
STATUS
approved