|
|
A166132
|
|
a(n) = 1 + (4*9^n - 9*4^n) / 5.
|
|
1
|
|
|
1, 37, 469, 4789, 45397, 417781, 3796885, 34319413, 309464533, 2787540085, 25097297941, 225913430197, 2033371866709, 18300950780149, 164710972940437, 1482408420140341, 13341714435968725, 120075584542541173
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
COMMENTS
|
Variable N_{LNR}(n) of the number of grid points triangulating snowflakes (Neuberger et al.).
|
|
LINKS
|
|
|
FORMULA
|
a(n) = 14*a(n-1) - 49*a(n-2) + 36*a(n-3).
G.f.: -x*(1+23*x) / ((x-1)*(4*x-1)*(9*x-1)).
E.g.f.: (1/5)*(5*exp(x) + 4*exp(9*x) - 9*exp(4*x)). - G. C. Greubel, Apr 26 2016
|
|
MAPLE
|
A := proc(n) 1+(4*9^n-9*4^n)/5 ; end proc: seq(A(n), n=1..60) ;
|
|
MATHEMATICA
|
LinearRecurrence[{14, -49, 36}, {1, 37, 469}, 50] (* G. C. Greubel, Apr 26 2016 *)
Table[1 + (4*9^n - 9*4^n)/5, {n, 24}] (* or *)
Rest@ CoefficientList[Series[-x (1 + 23 x)/((x - 1) (4 x - 1) (9 x - 1)), {x, 0, 24}], x] (* Michael De Vlieger, Apr 27 2016 *)
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|