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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.
2
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
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
KEYWORD
nonn,easy
AUTHOR
Luis Mantilla, Feb 28 2021
STATUS
approved