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 A218826 Number of indecomposable (by concatenation) alternating n-anagrams. 3
 1, 1, 4, 25, 217, 2470, 35647, 637129, 13843948, 360022957, 11054457253, 396003680518, 16377463914091, 774714094061221, 41572230979229284, 2512149910125036865, 169831839578092130017, 12769241823369505582150, 1062122471116082751430087, 97264621940872013476357969 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Alternating anagrams enumeration is related to A000366 by a(n) = A000366(n+1). For all n, a(n) are periodically congruent to 1, 1 and 4 modulo 6. LINKS Andrew Howroyd, Table of n, a(n) for n = 1..200 G. Kreweras and J. Barraud, Anagrammes alternés, European Journal of Combinatorics,Volume 18, Issue 8, November 1997, Pages 887-891. G. Kreweras and D. Dumont, Sur les anagrammes alternés, Discrete Mathematics, Volume 211, Issues 1-3, 28 January 2000, Pages 103-110. FORMULA G.f.: (1-Q(0))/x, where Q(k)= 1 - 1/2*(k+1)*(k+2)*x/(1 - 1/2*(k+1)*(k+2)*x/Q(k+1)); (continued fraction). - Sergei N. Gladkovskii, May 03 2013 G.f.: 1/Q(0), where Q(k) = 1 - (k+1)*(k+2)/2*x/(1 - (k+2)*(k+3)/2*x/Q(k+1) ; (continued fraction). - Sergei N. Gladkovskii, Nov 17 2013 a(n) = A000366(n + 1) - Sum_{k=2..n} A239894(n, k). - Andrew Howroyd, Feb 25 2020 PROG (PARI) a000366(n)= {return((-1/2)^(n-2)*sum(k=0, n, binomial(n, k)*(1-2^(n+k+1))*bernfrac(n+k+1))); } bi(n, k) = {if (matb[n, k] == 0, if (n==k, v=1, if (k==1, v = b(n), v = sum(i=1, n-k+1, b(i)*bi(n-i, k-1)); ); ); matb[n, k] = v; ); return (matb[n, k]); } b(n) = {if (n==1, return(a000366(n+1)), return(a000366(n+1) - sum(i=2, n, bi(n, i)))); } allb(m) = {matb = matrix(m, m); for (i=1, m, print1(b(i), ", "); ); } CROSSREFS Cf. A000366, A218827. First column of A239894. Sequence in context: A198198 A007830 A305404 * A060911 A060912 A209319 Adjacent sequences:  A218823 A218824 A218825 * A218827 A218828 A218829 KEYWORD nonn AUTHOR Michel Marcus, Nov 07 2012 STATUS approved

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Last modified November 30 09:18 EST 2021. Contains 349419 sequences. (Running on oeis4.)