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 A213284 Number of 5-length words w over n-ary alphabet such that for every prefix z of w we have #(z,a_i) = 0 or #(z,a_i) >= #(z,a_j) for all j>i and #(z,a_i) counts the occurrences of the i-th letter in z. 2
 0, 1, 14, 74, 276, 895, 2506, 6104, 13224, 26061, 47590, 81686, 133244, 208299, 314146, 459460, 654416, 910809, 1242174, 1663906, 2193380, 2850071, 3655674, 4634224, 5812216, 7218725, 8885526, 10847214, 13141324, 15808451, 18892370, 22440156, 26502304 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1). FORMULA a(n) = n*(94-204*n+155*n^2-45*n^3+6*n^4)/6. G.f.: x*(1+8*x+5*x^2+22*x^3+84*x^4)/(1-x)^6. EXAMPLE a(0) = 0: no word of length 5 is possible for an empty alphabet. a(1) = 1: aaaaa for alphabet {a}. a(2) = 14: aaaaa, aaaab, aaaba, aaabb, aabaa, aabab, aabba, abaaa, abaab, ababa, baaaa, baaab, baaba, bbbbb for alphabet {a,b}. MAPLE a:= n-> n*(94+(-204+(155+(-45+6*n)*n)*n)*n)/6: seq(a(n), n=0..40); CROSSREFS Row n=5 of A213276. Sequence in context: A328735 A279447 A205590 * A232377 A146563 A205583 Adjacent sequences:  A213281 A213282 A213283 * A213285 A213286 A213287 KEYWORD nonn,easy AUTHOR Alois P. Heinz, Jun 08 2012 STATUS approved

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Last modified May 28 21:37 EDT 2020. Contains 334690 sequences. (Running on oeis4.)