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 A265624 Array T(n,k): The number of words of length n in an alphabet of size k which do not contain 4 consecutive letters. 5
 1, 1, 2, 1, 4, 3, 0, 8, 9, 4, 0, 14, 27, 16, 5, 0, 26, 78, 64, 25, 6, 0, 48, 228, 252, 125, 36, 7, 0, 88, 666, 996, 620, 216, 49, 8, 0, 162, 1944, 3936, 3080, 1290, 343, 64, 9, 0, 298, 5676, 15552, 15300, 7710, 2394, 512, 81, 10, 0, 548, 16572, 61452 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 LINKS Table of n, a(n) for n=1..59. FORMULA T(2,k) = k^2. T(3,k) = k^3. T(4,k) = k*(k+1)*(k^2+3*k+3). T(5,k) = k*(k+1)*(k^3+4*k^2+6*k+2). T(6,k) = k*(k+1)^2*(k^3+4*k^2+6*k+1). G.f. of row k: k*x*(1+x+x^2)/(1+(1-k)*x*(x^2+x+1)). EXAMPLE 1 2 3 4 5 6 7 8 1 4 9 16 25 36 49 64 1 8 27 64 125 216 343 512 0 14 78 252 620 1290 2394 4088 0 26 228 996 3080 7710 16716 32648 0 48 666 3936 15300 46080 116718 260736 0 88 1944 15552 76000 275400 814968 2082304 0 162 5676 61452 377520 1645950 5690412 16629816 MAPLE A265624 := proc(n, k) local x; k*x*(1+x+x^2)/(1+(1-k)*x*(x^2+x+1)) ; coeftayl(%, x=0, n) ; end proc; seq(seq(A265624(d-k, k), k=1..d-1), d=2..10) ; CROSSREFS Cf. A135491 (column k=2), A181137 (k=3), A188714 (k=4), A265583 (not 2 consecutive letters), A265584 (not 3 consecutive letters). Sequence in context: A352548 A258090 A112157 * A332332 A335259 A093682 Adjacent sequences: A265621 A265622 A265623 * A265625 A265626 A265627 KEYWORD nonn,tabl,easy AUTHOR R. J. Mathar, Dec 10 2015 STATUS approved

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Last modified September 26 11:38 EDT 2023. Contains 365656 sequences. (Running on oeis4.)