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%I #26 Mar 05 2022 01:03:55
%S 1,4,10,20,36,62,106,184,328,602,1134,2180,4252,8374,16594,33008,
%T 65808,131378,262486,524668,1048996,2097614,4194810,8389160,16777816,
%U 33555082,67109566,134218484,268436268,536871782,1073742754,2147484640
%N Row sums of triangle A131923.
%H Muniru A Asiru, <a href="/A131924/b131924.txt">Table of n, a(n) for n = 0..600</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (5,-9,7,-2).
%F Binomial transform of (1, 3, 3, 1, 1, 1, ...).
%F a(n) = 2^n + n^2 + n. - _Michel Marcus_, Jul 18 2018
%F From _Colin Barker_, Jul 18 2018: (Start)
%F G.f.: (1 - x - x^2 - x^3) / ((1 - x)^3*(1 - 2*x)).
%F a(n) = 5*a(n-1) - 9*a(n-2) + 7*a(n-3) - 2*a(n-4) for n>3.
%F (End)
%e a(4) = 36 = sum of terms in row 4 of triangle A131923: (5 + 8 + 10 + 8 + 5).
%e a(4) = 36 = (1, 4, 6, 4, 1) dot (1, 3, 3, 1, 1) = (1 + 12 + 18 + 4 + 1).
%t Table[2^n + n^2 + n, {n, 0, 5!}] (* _Vladimir Joseph Stephan Orlovsky_, May 07 2010 *)
%t LinearRecurrence[{5,-9,7,-2},{1,4,10,20},40] (* _Harvey P. Dale_, Jul 22 2021 *)
%o (GAP) a:=List(List([0..32],n->List([0..n],k->Binomial(n,k)+n)),Sum); # _Muniru A Asiru_, Jul 17 2018
%o (PARI) Vec((1 - x - x^2 - x^3) / ((1 - x)^3*(1 - 2*x)) + O(x^40)) \\ _Colin Barker_, Jul 18 2018
%Y Cf. A131923.
%K nonn,easy
%O 0,2
%A _Gary W. Adamson_, Jul 29 2007
%E More terms from _Vladimir Joseph Stephan Orlovsky_, May 07 2010
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