|
|
A253853
|
|
a(n) = 1 + a(n-2)*a(n-3), with a(0) = a(1) = a(2) = 1.
|
|
3
|
|
|
1, 1, 1, 2, 2, 3, 5, 7, 16, 36, 113, 577, 4069, 65202, 2347814, 265306939, 153082168429, 622891345681347, 40613761521380428832, 95353557892558423217593864, 25297960567233966143149250083396705, 3872666660463510383775257066365338059531886849
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,4
|
|
LINKS
|
|
|
FORMULA
|
a(n+5) == a(n) (mod 2) for all n>=0.
a(n+7) == a(n) (mod 7) for all n>=7.
a(n) ~ c^(d^n), where c = 1.33114442478885300080049... and d = ((27 - 3*sqrt(69)) / 2)^(1/3) / 3 + ((9 + sqrt(69))/2)^(1/3) / 3^(2/3) = 1.324717957244746... is the root of the equation d^3 = d + 1. - Vaclav Kotesovec, Jan 17 2015
|
|
MATHEMATICA
|
RecurrenceTable[{a[n]==1+a[n-2]*a[n-3], a[0]==1, a[1]==1, a[2]==1}, a, {n, 0, 20}] (* Vaclav Kotesovec, Jan 17 2015 *)
|
|
PROG
|
(PARI) {a(n) = if( n<3, n>=0, 1 + a(n-2)*a(n-3))};
(Haskell)
a253853 n = a253853_list !! n
a253853_list = 1 : 1 : 1 : map (+ 1)
(zipWith (*) a253853_list $ tail a253853_list)
(Magma) I:=[1, 1, 1]; [n le 3 select I[n] else 1 + Self(n-2)*Self(n-3): n in [1..30]]; // Vincenzo Librandi, Jan 22 2015
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|