A086443 Expansion of x^2/((1-4*x)*(1-3*x)^2).

0, 0, 1, 10, 67, 376, 1909, 9094, 41479, 183412, 792697, 3367618, 14120011, 58605808, 241331965, 987648382, 4022338063, 16318934764, 66007533313, 266354656186, 1072779614035, 4314363685480, 17330677214341, 69552836627830

Offset

0,4

Comments

Second binomial transform of A000295. Binomial transform of A066810 (with two leading zeros).

a(n) is the number of n-digit sequences on 4 symbols that have at least two 0's. For ternary sequences see A066810 and for binary sequences see A000295. - Enrique Navarrete, Apr 15 2022

Links

Table of n, a(n) for n=0..23.

Index entries for linear recurrences with constant coefficients, signature (10,-33,36).

Formula

a(n) = 4^n - 3^n - n*3^(n-1).

E.g.f.: exp(3*x)*(exp(x)-x-1). - Enrique Navarrete, Apr 15 2022

Example

a(4)=67 since the sequences are the 12 permutations of the form 1000, 2000, 3000; the 18 permutations of the form 1100, 2200, 3300; the 36 permutations of the form 1200, 1300, 2300; and 0000. - Enrique Navarrete, Apr 15 2022

Crossrefs

Cf. A000295, A066810.

Sequence in context: A278090 A266443 A108275 * A172066 A026844 A026875

Adjacent sequences: A086440 A086441 A086442 * A086444 A086445 A086446

Keyword

easy,nonn

Author

Paul Barry, Jul 21 2003

Status

approved