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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-Fran├žois 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.)