A181106 Largest odd number strictly less than a square.

-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

Author

Jerzy Kocik (jkocik(AT)siu.edu), Oct 03 2010

Keywords

• easy
• sign

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).

Crossrefs

Equals minus A141354.

Cf. A120413 (Largest even number strictly less than a square).

Programs

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 *)

PARI

Vec(x*(x^3-x^2-5*x+1)/((x-1)^3*(x+1)) + O(x^100)) \\ Colin Barker, Jun 27 2015

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)

Extensions

Edited by Ray Chandler, Dec 05 2011