A166132 - OEIS

%I #18 Apr 28 2016 11:22:58

%S 1,37,469,4789,45397,417781,3796885,34319413,309464533,2787540085,

%T 25097297941,225913430197,2033371866709,18300950780149,

%U 164710972940437,1482408420140341,13341714435968725,120075584542541173

%N a(n) = 1 + (4*9^n - 9*4^n) / 5.

%C Variable N_{LNR}(n) of the number of grid points triangulating snowflakes (Neuberger et al.).

%H G. C. Greubel, <a href="/A166132/b166132.txt">Table of n, a(n) for n = 1..500</a>

%H John M. Neuberger, Nandor Sieben, James W. Swift, <a href="http://arxiv.org/abs/1010.0775"> Computing Eigenfunctions on the Koch Snowflake: A New Grid and Symmetry</a>, arXiv:1010.0775 [math.DS], 2010.

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (14,-49,36).

%F a(n) = 14*a(n-1) - 49*a(n-2) + 36*a(n-3).

%F G.f.: -x*(1+23*x) / ((x-1)*(4*x-1)*(9*x-1)).

%F a(n) = A002451(n-1) + 23*A002451(n-2).

%F E.g.f.: (1/5)*(5*exp(x) + 4*exp(9*x) - 9*exp(4*x)). - _G. C. Greubel_, Apr 26 2016

%p A := proc(n) 1+(4*9^n-9*4^n)/5 ; end proc: seq(A(n),n=1..60) ;

%t LinearRecurrence[{14, -49, 36}, {1, 37, 469}, 50] (* _G. C. Greubel_, Apr 26 2016 *)

%t Table[1 + (4*9^n - 9*4^n)/5, {n, 24}] (* or *)

%t 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 *)

%K nonn,easy

%O 1,2

%A _Jonathan Vos Post_, Oct 06 2010