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INVERT transform of A118434, = row sums of triangle A144182.
4

%I #14 Aug 21 2016 11:10:09

%S 1,1,3,9,11,17,35,57,91,161,275,457,779,1329,2243,3801,6459,10945,

%T 18547,31465,53355,90449,153379,260089,440987,747745,1267923,2149897,

%U 3645387,6181233,10481027,17771801,30134267,51096321,86639923,146908457,249101099

%N INVERT transform of A118434, = row sums of triangle A144182.

%C A118434 = row sums of the self-inverse triangle A118433 (a generator for the Rao Uppuluri-Carpenter numbers, A000587).

%C A144181 = row sums of triangle A144182.

%H Colin Barker, <a href="/A144181/b144181.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,2).

%F Equals row sums of triangle A144182 and INVERT transform of A118434: (1, 0, 2, 4, -4, 0, -8, -16, 16, 0, 32,...).

%F From _Colin Barker_, Aug 21 2016: (Start)

%F a(n) = a(n-1)+2*a(n-3) for n>3.

%F G.f.: (1+2*x^2+4*x^3) / (1-x-2*x^3).

%F (End)

%e a(3) = 9 = sum of row 3 terms, triangle A144182: (4 + 2 + 0 + 3).

%o (PARI) Vec((1+2*x^2+4*x^3)/(1-x-2*x^3) + O(x^40)) \\ _Colin Barker_, Aug 21 2016

%Y Cf. A118434.

%Y Cf. A144182, A000587.

%K nonn,easy

%O 0,3

%A _Gary W. Adamson_, Sep 13 2008

%E More terms from _Alois P. Heinz_, May 23 2015