A341896 a(n) is the number of words of length n over the alphabet {a,b,c} with an even number of appearances of the letter 'a' and the sum of appearances of the letters 'b' and 'c' add up to at most 3.

1, 2, 5, 14, 25, 90, 61, 294, 113, 690, 181, 1342, 265, 2314, 365, 3670, 481, 5474, 613, 7790, 761, 10682, 925, 14214, 1105, 18450, 1301, 23454, 1513, 29290, 1741, 36022, 1985, 43714, 2245, 52430, 2521, 62234, 2813, 73190, 3121, 85362, 3445, 98814, 3785, 113610

Offset

0,2

References

Rodrigo de Castro, Teoría de la computación, 2004, unilibros.

Links

Luis Mantilla, Table of n, a(n) for n = 0..46

Luis Mantilla, demonstration

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

Formula

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

G.f.: (10*x^7-13*x^6+46*x^5+11*x^4+6*x^3+x^2+2*x+1)/((x-1)^4*(x+1)^4).

a(n) = 2*n + 8*C(n,3) if n is odd, a(n) = 1 + 4*C(n,2) if n is even. - Alois P. Heinz, Mar 01 2021

Example

a(0) = 1 : the empty word.
a(1) = 2 : {b, c}.
a(2) = 5 : {aa, bb, cc, bc, cb}.
a(3) = 14 : {aab, aac, aba, aca, baa, bbb, bbc, bcb, bcc, caa, cbb, cbc, ccb, bbb}.
a(4) = 25 : {aaaa, aabb, aabc, aacb, aacc, abab, abac, abba, abca, acab, acac, acba, baab, baac, baba, baca, bbaa, bcaa, caab, caac, caba, caca, cbaa, ccaa, acca}.

Crossrefs

Bisection gives: A080856 (even part).

Sequence in context: A290414 A288905 A289040 * A214203 A100779 A212346

Adjacent sequences: A341893 A341894 A341895 * A341897 A341898 A341899

Keyword

nonn,easy

Author

Luis Mantilla, Feb 28 2021

Status

approved