A362316 Expansion of e.g.f (exp(x)-1)*(exp(2*x)-1).

0, 0, 4, 18, 64, 210, 664, 2058, 6304, 19170, 58024, 175098, 527344, 1586130, 4766584, 14316138, 42981184, 129009090, 387158344, 1161737178, 3485735824, 10458256050, 31376865304, 94134790218, 282412759264, 847255055010, 2541798719464, 7625463267258, 22876524019504, 68629840493970

Offset: 0

Author

Enrique Navarrete, Apr 16 2023

Keywords

• nonn
• easy

Comments

Number of ternary strings with at least one 0 or one 1 and at least one 2.

Examples

			The 4 strings for n=4 are 12, 21, 02, 20.
		

Links

• Paolo Xausa, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (6,-11,6).

Crossrefs

Cf. A001550, A053152, A083321 (alternates signs).

Programs

Mathematica

LinearRecurrence[{6,-11,6},{0,0,4,18},30] (* Paolo Xausa, Aug 07 2023 *)

Formula

a(n) = 3^n - 2^n - 1, n>0; a(0)=0.

a(n) = 2*A053152(n).