cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A166132 a(n) = 1 + (4*9^n - 9*4^n) / 5.

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%I A166132 #18 Apr 28 2016 11:22:58
%S A166132 1,37,469,4789,45397,417781,3796885,34319413,309464533,2787540085,
%T A166132 25097297941,225913430197,2033371866709,18300950780149,
%U A166132 164710972940437,1482408420140341,13341714435968725,120075584542541173
%N A166132 a(n) = 1 + (4*9^n - 9*4^n) / 5.
%C A166132 Variable N_{LNR}(n) of the number of grid points triangulating snowflakes (Neuberger et al.).
%H A166132 G. C. Greubel, <a href="/A166132/b166132.txt">Table of n, a(n) for n = 1..500</a>
%H A166132 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 A166132 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (14,-49,36).
%F A166132 a(n) = 14*a(n-1) - 49*a(n-2) + 36*a(n-3).
%F A166132 G.f.: -x*(1+23*x) / ((x-1)*(4*x-1)*(9*x-1)).
%F A166132 a(n) = A002451(n-1) + 23*A002451(n-2).
%F A166132 E.g.f.: (1/5)*(5*exp(x) + 4*exp(9*x) - 9*exp(4*x)). - _G. C. Greubel_, Apr 26 2016
%p A166132 A := proc(n) 1+(4*9^n-9*4^n)/5 ; end proc: seq(A(n),n=1..60) ;
%t A166132 LinearRecurrence[{14, -49, 36}, {1, 37, 469}, 50] (* _G. C. Greubel_, Apr 26 2016 *)
%t A166132 Table[1 + (4*9^n - 9*4^n)/5, {n, 24}] (* or *)
%t A166132 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 A166132 nonn,easy
%O A166132 1,2
%A A166132 _Jonathan Vos Post_, Oct 06 2010