[seqfan] Re: Two sequences, one new, in Computing Eigenfunctions on the Koch Snowflake

[Richard Mathar]

http://list.seqfan.eu/pipermail/seqfan/2010-October/006167.html

jvp> John M. Neuberger, Nandor Sieben, James W. Swift,
jvp> Computing Eigenfunctions on the Koch Snowflake: A New Grid and Symmetry
jvp> http://arxiv.org/abs/1010.0775
jvp> 
jvp> is: [for n>0]
jvp> A016153   (9^n-4^n)/5.
jvp> 
jvp> The second row is:
jvp> 1, 37, 469, 4789, 45397, 417781
jvp> 
jvp> which is not in OEIS.

This could look roughly as follows:

%I A000001
%S A000001 1,37,469,4789,45397,417781,3796885,34319413,309464533,2787540085,
%T A000001 25097297941,225913430197,2033371866709,18300950780149,164710972940437,
%U A000001 1482408420140341,13341714435968725,120075584542541173,1080680879358161173
%N A000001 1+(4*9^n-9*4^n)/5.
%C A000001 Variable N_{LNR}(n) of the number of grid points triangulating snow flakes (Neuberger et al).
%H A000001 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
%H A000001 <a href="Sindx_Rea.html#recLCC">Index to sequences with linear recurrences with constant coefficients</a>, signature (14,-49,36).
%F A000001 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) ).
%F A000001 a(n)= A002451(n-1)+23*A002451(n-2).
%p A000001 A := proc(n) 1+(4*9^n-9*4^n)/5 ; end proc: seq(A(n),n=1..60) ;
%K A000001 nonn,easy
%O A000001 1,2
%A A000001 Jonathan Post (jvospost3(AT)gmail.com), Oct 06 2010