A132734 - OEIS

%I #11 Feb 14 2021 18:39:22

%S 1,2,5,16,43,102,225,476,983,2002,4045,8136,16323,32702,65465,130996,

%T 262063,524202,1048485,2097056,4194203,8388502,16777105,33554316,

%U 67108743,134217602,268435325,536870776,1073741683,2147483502,4294967145,8589934436,17179869023

%N Row sums of triangle A132733.

%H Andrew Howroyd, <a href="/A132734/b132734.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 (4,-5,2)

%F Binomial transform of [1, 1, 2, 6, 2, 6, 2, 6, ...].

%F From _Andrew Howroyd_, Sep 01 2018: (Start)

%F a(n) = 4*2^n - 5*n - 1 for n > 0.

%F a(n) = 4*a(n-1) - 5*a(n-2) + 2*a(n-3) for n > 3.

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

%F E.g.f.: -2 - (1 + 5*x)*exp(x) + 4*exp(2*x). - _G. C. Greubel_, Feb 14 2021

%e a(3) = 16 = sum of row 3 terms of triangle A132733: (1 + 7 + 7 + 1).

%e a(3) = 16 = (1, 3, 3, 1) dot (1, 1, 2, 6) = (1 + 3 + 6 + 6).

%t Table[2^(n+2) -(5*n+1) -2*Boole[n==0], {n,0,30}] (* _G. C. Greubel_, Feb 14 2021 *)

%o (PARI) a(n)={if(n==0, 1, 4*2^n - 5*n - 1)} \\ _Andrew Howroyd_, Sep 01 2018

%o (PARI) Vec((1 - 2*x + 2*x^2 + 4*x^3)/((1 - x)^2*(1 - 2*x)) + O(x^40)) \\ _Andrew Howroyd_, Sep 01 2018

%o (Sage) [1]+[2^(n+2) -(5*n +1) for n in (1..30)] # _G. C. Greubel_, Feb 14 2021

%o (Magma) [1] cat [2^(n+2) -(5*n +1): n in [1..30]]; // _G. C. Greubel_, Feb 14 2021

%Y Cf. A132733.

%K nonn,easy

%O 0,2

%A _Gary W. Adamson_, Aug 26 2007

%E Terms a(10) and beyond from _Andrew Howroyd_, Sep 01 2018