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 A115866 a(n) = g(n,n,n) where g(a, b, c) is defined as follows: if a = 0 or b = 0 or c = 0 then return 1 otherwise return g(a, b, c-1) + g(a, b-1, c) + g(a-1, b, c) + g(a, b-1, c-1) + g(a-1, b, c-1) + g(a-1, b-1, c) + g(a-1, b-1, c-1). 3
 1, 7, 157, 5419, 220561, 9763807, 454635973, 21894817147, 1080094827649, 54250971690007, 2763339510402637, 142338478909290187, 7399210542653679985, 387578046480606144079, 20433042381373273363477, 1083193405190852829195259, 57697563083258107660231681 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS A generalization of the recurrence in A001850. The original description of this sequence was the same as that of A126086. The correct explanation for these terms was provided by Nick Hobson (nickh(AT)qbyte.org), Mar 03 2007. LINKS Alois P. Heinz, Table of n, a(n) for n = 0..500 FORMULA D-finite with recurrence: 2*(n-1)^2*(2*n-1)*(243*n^5 - 3159*n^4 + 16254*n^3 - 41325*n^2 + 51838*n - 25620)*a(n) = (53703*n^8 - 887922*n^7 + 6273882*n^6 - 24692601*n^5 + 59070956*n^4 - 87717383*n^3 + 78694087*n^2 - 38816698*n + 8003688)*a(n-1) + (94527*n^8 - 1549611*n^7 + 10848681*n^6 - 42278007*n^5 + 100087538*n^4 - 147021644*n^3 + 130465402*n^2 - 63678226*n + 13003980)*a(n-2) - (31833*n^8 - 541890*n^7 + 3945213*n^6 - 16007835*n^5 + 39486422*n^4 - 60435299*n^3 + 55812796*n^2 - 28273516*n + 5965068)*a(n-3) + (n-3)*(3159*n^7 - 48114*n^6 + 301212*n^5 - 1002003*n^4 + 1908157*n^3 - 2073535*n^2 + 1184960*n - 272792)*a(n-4) - 2*(n-4)^2*(n-3)*(243*n^5 - 1944*n^4 + 6048*n^3 - 9087*n^2 + 6529*n - 1769)*a(n-5). - Vaclav Kotesovec, Nov 27 2016 a(n) ~ (12*2^(2/3)+15*2^(1/3)+19)^n / (2^(4/3)*3^(1/2)*Pi*n). - Vaclav Kotesovec, Nov 27 2016 MAPLE g():= seq(convert(n, base, 2)[1..3], n=9..15): b:= proc(l) option remember;       `if`(l[1]=0, 1, add(b(sort(l-h)), h=g()))     end: a:= n-> b([n\$3]): seq(a(n), n=0..25);  # Alois P. Heinz, Oct 14 2015 MATHEMATICA g[] = Table[Reverse[IntegerDigits[n, 2]][[;; 3]], {n, 2^3 + 1, 2^4 - 1}]; b[l_] := b[l] = If[l[[1]] == 0, 1, Sum[b[Sort[l - h]], {h, g[]}]]; a[n_] := b[Table[n, {3}]]; a /@ Range[0, 25] (* Jean-François Alcover, Apr 25 2020, after Alois P. Heinz *) CROSSREFS Cf. A001850, A126086. Column k=3 of A263159. Sequence in context: A197979 A203584 A073605 * A197766 A009703 A014385 Adjacent sequences:  A115863 A115864 A115865 * A115867 A115868 A115869 KEYWORD nonn AUTHOR Al Zimmermann, Apr 02 2006 EXTENSIONS Edited by N. J. A. Sloane following email from Nick Hobson (nickh(AT)qbyte.org), Mar 03 2007 More terms from Alois P. Heinz, Sep 30 2015 STATUS approved

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Last modified January 24 17:28 EST 2022. Contains 350565 sequences. (Running on oeis4.)