A342159 Number of words of length n, over the alphabet {a,b,c}, which have an odd number of a's and the number of b's plus the number of c's is less than or equal to 3.

0, 1, 4, 13, 40, 41, 172, 85, 464, 145, 980, 221, 1784, 313, 2940, 421, 4512, 545, 6564, 685, 9160, 841, 12364, 1013, 16240, 1201, 20852, 1405, 26264, 1625, 32540, 1861, 39744, 2113, 47940, 2381, 57192, 2665, 67564, 2965, 79120, 3281, 91924, 3613, 106040, 3961, 121532, 4325, 138464, 4705, 156900

Offset

0,3

References

Rodrigo De Castro, Teoria de la computación [Computer Theory], book published by National University of Colombia [date?].

Links

Table of n, a(n) for n=0..50.

Index entries for linear recurrences with constant coefficients, signature (0,4,0,-6,0,4,0,-1).

Formula

a(n) = (14/3)*n - 4*n^2 + (4/3)*n^3 if n is even;

a(n) = 1 - 2*n + 2*n^2 if n is odd.

From Chai Wah Wu, Mar 04 2021: (Start)

a(n) = 4*a(n-2) - 6*a(n-4) + 4*a(n-6) - a(n-8) for n > 7.

G.f.: x*(-x^3 + 7*x^2 + x + 1)*(5*x^3 - x^2 + 3*x + 1)/((x - 1)^4*(x + 1)^4). (End)

Crossrefs

Sequence in context: A000746 A271012 A272581 * A191132 A360606 A119915

Adjacent sequences: A342156 A342157 A342158 * A342160 A342161 A342162

Keyword

nonn,easy

Author

Marlon Vanegas, Mar 02 2021

Status

approved