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Row sums of triangle A133085.
2

%I #17 Mar 07 2022 00:02:42

%S 1,4,10,26,64,152,352,800,1792,3968,8704,18944,40960,88064,188416,

%T 401408,851968,1802240,3801088,7995392,16777216,35127296,73400320,

%U 153092096,318767104,662700032,1375731712,2852126720,5905580032,12213813248,25232932864

%N Row sums of triangle A133085.

%H G. C. Greubel, <a href="/A133086/b133086.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (4,-4).

%F Binomial transform of A114753: (1, 3, 3, 7, 5, 11, 7, 15, ...).

%F For n>1, a(n) = 2^n + 3*n*2^(n-2). - _R. J. Mathar_, Apr 04 2012

%e a(3) = 26 = sum of row 3 of triangle A133085: (12 + 8, + 5 + 1).

%e a(3) = 26 = (1, 3, 3, 1) dot (1, 3, 3, 7) = (1 + 9 + 9 + 7).

%t Join[{1, 4}, Table[2^n + 3*n*2^(n - 2), {n, 2, 50}]] (* _G. C. Greubel_, Oct 21 2017 *)

%t LinearRecurrence[{4,-4},{1,4,10,26},40] (* _Harvey P. Dale_, Jul 19 2020 *)

%o (PARI) concat([1,4], for(n=2,50, print1(2^n + 3*n*2^(n-2), ", "))) \\ _G. C. Greubel_, Oct 21 2017

%o (Magma) [1,4] cat [2^n+3*n*2^(n-2): n in [2..30]]; // _Vincenzo Librandi_, Oct 21 2017

%Y Cf. A133085, A114753, A133080.

%K nonn

%O 0,2

%A _Gary W. Adamson_, Sep 08 2007