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URL: https://oeis.org/A392334

⇱ A392334 - OEIS

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A392334
a(2*n) = 2*n+1, a(2*n+1) = (2*n+1)^2.
1
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
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).
Sequence in context: A262024 A252117 A103934 * A365203 A186814 A077384
KEYWORD
nonn,easy
AUTHOR
Paul Barry, Jan 07 2026
STATUS
approved