A392334 a(2*n) = 2*n+1, a(2*n+1) = (2*n+1)^2.

1, 1, 3, 9, 5, 25, 7, 49, 9, 81, 11, 121, 13, 169, 15, 225, 17, 289, 19, 361, 21, 441, 23, 529, 25, 625, 27, 729, 29, 841, 31, 961, 33, 1089, 35, 1225, 37, 1369, 39, 1521, 41, 1681, 43, 1849, 45, 2025, 47, 2209, 49, 2401, 51, 2601, 53, 2809, 55, 3025, 57, 3249

Offset

0,3

Links

Paolo Xausa, Table of n, a(n) for n = 0..10000

Index entries for linear recurrences with constant coefficients, signature (0,3,0,-3,0,1).

Formula

G.f.: (1 + x + 6*x^3 - x^4 + x^5)/(1 - x^2)^3.

E.g.f.: (1 + x)*(cosh(x) + x*sinh(x)).

a(n) = (1 + n + n^2 + (-1)^n*(1 + n - n^2))/2. - Stefano Spezia, Jan 07 2026

a(n) = A109613(n)^A000034(n). - Alois P. Heinz, Jan 07 2026

Maple

a:= n-> (d-> (n-d+2)^d)(n mod 2+1):
seq(a(n), n=0..57);  # Alois P. Heinz, Jan 07 2026

Mathematica

Riffle[#, #^2] & [Range[1, 100, 2]] (* Paolo Xausa, Jan 07 2026 *)
LinearRecurrence[{0, 3, 0, -3, 0, 1}, {1, 1, 3, 9, 5, 25}, 60] (* Harvey P. Dale, Mar 15 2026 *)

Crossrefs

Bisections give: A005408, A016754.

Partial sums are A228958(n+1).

Cf. A000034, A109613.

Sequence in context: A262024 A252117 A103934 * A365203 A186814 A077384

Adjacent sequences: A392331 A392332 A392333 * A392335 A392336 A392337

Keyword

nonn,easy

Author

Paul Barry, Jan 07 2026

Status

approved