A383608 Expansion of e.g.f. (1+x)*cosh(x)^2.

1, 1, 2, 6, 8, 40, 32, 224, 128, 1152, 512, 5632, 2048, 26624, 8192, 122880, 32768, 557056, 131072, 2490368, 524288, 11010048, 2097152, 48234496, 8388608, 209715200, 33554432, 905969664, 134217728, 3892314112, 536870912, 16642998272, 2147483648, 70866960384, 8589934592

Offset: 0

Author

Enrique Navarrete, May 01 2025

Keywords

• nonn
• easy

Comments

a(n) is the number of ternary strings of length n with an even number of 0s and 2s and one or no 1s.

A081294 and A229580 interleaved.

Examples

			a(5)=40 since the strings are the 30 permutations of 00221, the 5 permutations of 00001, and the 5 permutations of 22221.
		

Links

• Index entries for linear recurrences with constant coefficients, signature (0,8,0,-16).

Crossrefs

Cf. A081294, A229580.

Formula

a(n)=2^(n-1) for n even, n > 0, a(0)=1.

a(n)=n*2^(n-2) for n odd, n > 1, a(1)=1.

G.f.: (1 + x - 6*x^2 - 2*x^3 + 8*x^4 + 8*x^5)/(1 - 4*x^2)^2. - Stefano Spezia, May 02 2025

a(n) = 8*a(n-2) - 16*a(n-4), n > 5.