A390255 Expansion of e.g.f. x*(1 + x/2)*sinh(x).

0, 0, 2, 3, 4, 10, 6, 21, 8, 36, 10, 55, 12, 78, 14, 105, 16, 136, 18, 171, 20, 210, 22, 253, 24, 300, 26, 351, 28, 406, 30, 465, 32, 528, 34, 595, 36, 666, 38, 741, 40, 820, 42, 903, 44, 990, 46, 1081, 48, 1176, 50, 1275, 52, 1378, 54, 1485, 56, 1596, 58, 1711, 60

Offset

0,3

Comments

Even numbers and second hexagonal numbers interleaved.

Number of binary strings of length n with one or two 0's and an odd number of 1's.

Number of ternary strings of length n with either one 0 or two 2's and an odd number of 1's.

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

a(n) = n, n even; a(n) = binomial(n,2), n odd.

G.f.: x^2*(2 + 3*x - 2*x^2 + x^3)/(1 - x^2)^3. - Stefano Spezia, Oct 30 2025

Example

a(6) = 6 since the strings are the 6 permutations of 111110.
a(7) = 21 since the strings are the 21 permutations of 1111122.

Mathematica

A390255[n_] := If[OddQ[n], Binomial[n, 2], n]; Array[A390255, 100, 0] (* Paolo Xausa, Jan 02 2026 *)

Crossrefs

Cf. A014105.

Sequence in context: A241083 A334463 A143178 * A084190 A377484 A380967

Adjacent sequences: A390252 A390253 A390254 * A390256 A390257 A390258

Keyword

nonn,easy

Author

Enrique Navarrete, Oct 30 2025

Status

approved