A341705 a(n) = 70*binomial(n,8) + 2*binomial(n,4) + 1.

1, 1, 1, 1, 3, 11, 31, 71, 211, 883, 3571, 12211, 35641, 91521, 212213, 453181, 904541, 1706461, 3069181, 5298493, 8827591, 14256271, 22398531, 34339691, 51504223, 75735551, 109389151, 155440351, 217608301, 300497653, 409759561, 552273681, 736352921, 971972761

Offset

0,5

Comments

a(n) is the number of ternary strings of length n that contain either none or four 0's and either none or four 1's.

Links

Table of n, a(n) for n=0..33.

Index entries for linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,1).

Formula

E.g.f.: exp(x)*(1 + x^4/24)^2.

O.g.f.:(1 - 8*x + 28*x^2 - 56*x^3 + 72*x^4 - 64*x^5 + 40*x^6 - 16*x^7 + 73*x^8)/(1 - x)^9. - Stefano Spezia, Feb 19 2021

Example

a(9)=883 since the strings are the 630 permutations of 000011112, the 126 permutations of 000022222, the 126 permutations of 111122222, and 222222222.

Crossrefs

Cf. A341703, A341704.

Sequence in context: A107587 A245931 A190590 * A241693 A087323 A236752

Adjacent sequences: A341702 A341703 A341704 * A341706 A341707 A341708

Keyword

nonn,easy

Author

Enrique Navarrete, Feb 17 2021

Status

approved