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%I #15 Jul 12 2017 16:36:10
%S 1,4,5,12,17,32,49,84,133,220,353,576,929,1508,2437,3948,6385,10336,
%T 16721,27060,43781,70844,114625,185472,300097,485572,785669,1271244,
%U 2056913,3328160,5385073,8713236,14098309,22811548,36909857,59721408,96631265,156352676
%N Row sums of triangle A131327.
%C a(n)/a(n-1) tends to phi. (Cf. A062114).
%H Colin Barker, <a href="/A131328/b131328.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (1,2,-1,-1).
%F a(n+1) = A131326(n) + A052952(n+1).
%F a(n) = -3*(1+(-1)^n)/2 +4*A000045(n+1). - _R. J. Mathar_, Aug 13 2012
%F G.f.: ( 1+3*x-x^2 ) / ( (x-1)*(1+x)*(x^2+x-1) ). - _R. J. Mathar_, Aug 13 2012
%F From _Colin Barker_, Jul 12 2017: (Start)
%F a(n) = (2^(1-n)*((1+sqrt(5))^(n+1) - (1-sqrt(5))^(n+1))) / sqrt(5) - 3 for n even.
%F a(n) = (2^(1-n)*((1+sqrt(5))^(n+1) - (1-sqrt(5))^(n+1))) / sqrt(5) for n odd.
%F a(n) = a(n-1) + 2*a(n-2) - a(n-3) - a(n-4) for n>3.
%F (End)
%e a(3) = 12 = sum of row 3 terms of A131327: (3 + 5 + 3 + 1).
%e a(3) = (9 + 3) since we add terms of A131326: (1, 3, 4, 9, 13,...) to A052952: (0, 1, 1, 3, 4,...), getting (9 + 3 ) = 12.
%o (PARI) Vec((1 + 3*x - x^2) / ((1 - x)*(1 + x)*(1 - x - x^2)) + O(x^50)) \\ _Colin Barker_, Jul 12 2017
%Y Cf. A062114, A052952, A131324, A131325, A131326, A131327.
%K nonn,easy
%O 0,2
%A _Gary W. Adamson_, Jun 28 2007
%E More terms from _Colin Barker_, Jul 12 2017
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