A382640 a(n) = 90*binomial(n,6) + 90*binomial(n,5) + 54*binomial(n,4) + 24*binomial(n,3) + 9*binomial(n,2) + 3*n + 1.

1, 4, 16, 61, 217, 706, 2074, 5461, 12961, 28072, 56236, 105469, 187081, 316486, 514102, 806341, 1226689, 1816876, 2628136, 3722557, 5174521, 7072234, 9519346, 12636661, 16563937, 21461776, 27513604, 34927741, 43939561, 54813742, 67846606, 83368549, 101746561

Offset: 0

Author

Enrique Navarrete, Apr 01 2025

Keywords

• nonn
• easy

Comments

a(n) is the number of words of length n defined on 4 symbols where three chosen symbols (say, the three largest ones) are used at most twice.

Examples

			a(3) = 61 since from the 64 words defined on {0, 1, 2, 3} we subtract the three words 111, 222, 333.
		

Links

• Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

Crossrefs

Cf. A382618.

Formula

a(n) = 37 - 94*(n+1) + (187/2)*(n+1)^2 - (373/8)*(n+1)^3 + (103/8)*(n+1)^4 - (15/8)*(n+1)^5 + (1/8)*(n+1)^6.

E.g.f.: (1 + x + x^2/2)^3*exp(x).

G.f.: (1 - 3*x + 9*x^2 - 2*x^3 + 21*x^4 + 27*x^5 + 37*x^6)/(1 - x)^7. - Stefano Spezia, Apr 01 2025