A213037 a(n) = n^2 - 2*floor(n/2)^2.

0, 1, 2, 7, 8, 17, 18, 31, 32, 49, 50, 71, 72, 97, 98, 127, 128, 161, 162, 199, 200, 241, 242, 287, 288, 337, 338, 391, 392, 449, 450, 511, 512, 577, 578, 647, 648, 721, 722, 799, 800, 881, 882, 967, 968, 1057, 1058, 1151, 1152, 1249, 1250, 1351

Offset: 0

Author

Clark Kimberling, Jun 06 2012

Keywords

• nonn
• easy

Links

• David Lovler, Table of n, a(n) for n = 0..10000
• Index entries for linear recurrences with constant coefficients, signature (1,2,-2,-1,1).

Crossrefs

Cf. A000290, A008794.

Cf. A247375.

Cf. A322630 (diagonal).

Programs

Mathematica

a[n_] := n^2 - 2 Floor[n/2]^2
Table[a[n], {n, 0, 90}]    (* A213037 *)
LinearRecurrence[{1,2,-2,-1,1},{0,1,2,7,8},60] (* Harvey P. Dale, Oct 06 2016 *)

PARI

a(n) = n^2 - 2*(n\2)^2; \\ Michel Marcus, May 25 2022

Formula

a(n) = a(n-1) + 2*a(n-2) - 2*a(n-3) - a(n-4) + a(n-5).

G.f.: x*(1 + x + 3*x^2 - x^3)/((1 - x)^3*(1 + x)^2). [Corrected by Bruno Berselli, Sep 16 2014]

a(n) = A000290(n) - 2*A008794(n). - Michel Marcus, May 27 2022

E.g.f.: ((3*x + x^2)*cosh(x) + (-1 + x + x^2)*sinh(x))/2. - David Lovler, Jun 20 2022

Sum_{n>=1} 1/a(n) = Pi^2/12 - cot(Pi/sqrt(2))*Pi/(2*sqrt(2)) + 1/2. - Amiram Eldar, Sep 24 2022