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, 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
KEYWORD
nonn
AUTHOR
Al Zimmermann, Apr 02 2006
EXTENSIONS
Edited by N. J. A. Sloane following email from Nick Hobson, Mar 03 2007
More terms from Alois P. Heinz, Sep 30 2015
STATUS
approved