A374098 a(n) = A112387(n)^2.

1, 1, 4, 1, 16, 9, 64, 25, 256, 121, 1024, 441, 4096, 1849, 16384, 7225, 65536, 29241, 262144, 116281, 1048576, 466489, 4194304, 1863225, 16777216, 7458361, 67108864, 29822521, 268435456, 119311929, 1073741824, 477204025, 4294967296, 1908903481, 17179869184

Offset: 0

Author

Paul Curtz, Jun 28 2024

Keywords

• nonn
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (0,3,0,6,0,-8).

Crossrefs

Cf. A000302, A003683, A084175, A112387, A139818.

Programs

Mathematica

LinearRecurrence[{0, 3, 0, 6, 0, -8}, {1, 1, 4, 1, 16, 9}, 35] (* Amiram Eldar, Jul 01 2024 *)

Formula

a(2*n) = A000302(n); a(2*n+1) = A139818(n+1).

(a(2*n) + a(2*n-1))^2 = A084175(n+1)^2 + 16*A003683(n)^2, for n >= 1. - Thomas Scheuerle, Jun 28 2024

G.f. ( 1+x+x^2-2*x^3-2*x^4 ) / ( (x-1)*(2*x+1)*(2*x-1)*(1+x)*(2*x^2+1) ). - R. J. Mathar, Aug 02 2024