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

0,3

Comments

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

Links

Paolo Xausa, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (6,-11,6).

Formula

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

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

Example

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

Mathematica

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

Crossrefs

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

Sequence in context: A212766 A100177 A083321 * A255611 A022728 A231950

Adjacent sequences: A362313 A362314 A362315 * A362317 A362318 A362319

Keyword

nonn,easy

Author

Enrique Navarrete, Apr 16 2023

Status

approved