A354594 a(n) = n^2 + 2*floor(n/2)^2.

0, 1, 6, 11, 24, 33, 54, 67, 96, 113, 150, 171, 216, 241, 294, 323, 384, 417, 486, 523, 600, 641, 726, 771, 864, 913, 1014, 1067, 1176, 1233, 1350, 1411, 1536, 1601, 1734, 1803, 1944, 2017, 2166, 2243, 2400, 2481, 2646, 2731, 2904

Offset: 0

Author

David Lovler, Jun 01 2022

Keywords

• nonn
• easy

Comments

The first bisection is A033581, the second bisection is A080859. - Bernard Schott, Jun 07 2022

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, A033581, A080859, A247375.

Cf. A213037, A322744 (diagonal), A354595, A354596.

Programs

Mathematica

a[n_] := n^2 + 2 Floor[n/2]^2
Table[a[n], {n, 0, 90}]    (* A354594 *)
LinearRecurrence[{1, 2, -2, -1, 1}, {0, 1, 6, 11, 24}, 60]

PARI

a(n) = n^2 + 2*(n\2)^2;

Formula

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

a(n) = A000290(n) + 2*A008794(n).

G.f.: x*(1 + 5*x + 3*x^2 + 3*x^3)/((1 - x)^3*(1 + x)^2).

E.g.f.: (x*(1 + 3*x)*cosh(x) + (1 + 3*x + 3*x^2)*sinh(x))/2. - Stefano Spezia, Jun 07 2022