login
A181106
Largest odd number strictly less than a square.
2
-1, 3, 7, 15, 23, 35, 47, 63, 79, 99, 119, 143, 167, 195, 223, 255, 287, 323, 359, 399, 439, 483, 527, 575, 623, 675, 727, 783, 839, 899, 959, 1023, 1087, 1155, 1223, 1295, 1367, 1443, 1519, 1599, 1679, 1763, 1847, 1935, 2023, 2115, 2207, 2303, 2399, 2499
OFFSET
1,2
COMMENTS
The terms are the negatives of A141354 and therefore have the same generating function except the sign.
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
Equals minus A141354.
Cf. A120413 (Largest even number strictly less than a square).
Sequence in context: A067317 A349743 A141354 * A131753 A330319 A171503
KEYWORD
easy,sign
AUTHOR
Jerzy Kocik (jkocik(AT)siu.edu), Oct 03 2010
EXTENSIONS
Edited by Ray Chandler, Dec 05 2011
STATUS
approved