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%I #21 Jul 08 2022 09:04:28
%S 1,3,9,30,100,330,1089,3597,11881,39240,129600,428040,1413721,4669203,
%T 15421329,50933190,168220900,555595890,1835008569,6060621597,
%U 20016873361,66111241680,218350598400,721163036880,2381839709041
%N a(n) = 3*a(n-1) + 3*a(n-3) + a(n-4).
%H Michael De Vlieger, <a href="/A089931/b089931.txt">Table of n, a(n) for n = 0..1927</a>
%H Andreas M. Hinz and Paul K. Stockmeyer, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL25/Hinz/hinz5.html">Precious Metal Sequences and Sierpinski-Type Graphs</a>, J. Integer Seq., Vol 25 (2022), Article 22.4.8.
%H <a href="/index/Ch#Cheby">Index entries for sequences related to Chebyshev polynomials.</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (3,0,3,1).
%F a(n) = ((3 + sqrt(13)^n(11 + 3*sqrt(13))/13 + (3 - sqrt(13)^n(11 - 3*sqrt(13))/13)*2^(-1 - n) + 2(-1)^n/13;
%F a(n) = (-i)^n*Sum_{k=0..floor(n/2)} U(n-2k, 3i/2) where i = sqrt(-1).
%F G.f.: -1 / ( (1+x^2)*(x^2+3*x-1) ). - _R. J. Mathar_, Feb 14 2015
%t LinearRecurrence[{3,0,3,1},{1,3,9,30},30] (* _Harvey P. Dale_, Jun 16 2015 *)
%Y Cf. A006498.
%K easy,nonn
%O 0,2
%A _Paul Barry_, Nov 15 2003
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