OFFSET
0,1
COMMENTS
LINKS
Colin Barker, Table of n, a(n) for n = 0..1000
Wikipedia, Sierpinski triangle, see section on higher dimensional analogs.
Index entries for linear recurrences with constant coefficients, signature (13,-56,92,-48).
FORMULA
From Colin Barker, Jan 28 2017: (Start)
a(n) = 13*a(n-1) - 56*a(n-2) + 92*a(n-3) - 48*a(n-4) for n>3.
G.f.: (5 - 51*x + 153*x^2 - 122*x^3) / ((1 - x)*(1 - 2*x)*(1 - 4*x)*(1 - 6*x)).
(End)
MAPLE
A281698:=n->5*2^(n-1) + 2^(2*n-1) + 6^n + 1: seq(A281698(n), n=0..30); # Wesley Ivan Hurt, Apr 09 2017
MATHEMATICA
Table[5*2^(n - 1) + 2^(2 n - 1) + 6^n + 1, {n, 0, 22}] (* or *)
LinearRecurrence[{13, -56, 92, -48}, {5, 14, 55, 269}, 23] (* or *)
CoefficientList[Series[(5 - 51 x + 153 x^2 - 122 x^3)/((1 - x) (1 - 2 x) (1 - 4 x) (1 - 6 x)), {x, 0, 22}], x] (* Michael De Vlieger, Jan 28 2017 *)
PROG
(PARI) Vec((5 - 51*x + 153*x^2 - 122*x^3) / ((1 - x)*(1 - 2*x)*(1 - 4*x)*(1 - 6*x)) + O(x^30)) \\ Colin Barker, Jan 28 2017
(PARI) a(n) = 5*2^(n-1) + 2^(2*n-1) + 6^n + 1 \\ Charles R Greathouse IV, Jan 29 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Steven Beard, Jan 27 2017
STATUS
approved