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%I #35 May 13 2022 05:16:21
%S 1,3,7,14,28,56,112,224,448,896,1792,3584,7168,14336,28672,57344,
%T 114688,229376,458752,917504,1835008,3670016,7340032,14680064,
%U 29360128,58720256,117440512,234881024,469762048,939524096,1879048192,3758096384,7516192768,15032385536
%N Row sums of A125175.
%H Vincenzo Librandi, <a href="/A125176/b125176.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (2).
%F a(1) = 1, a(2) = 3, a(n) = 7*2^(n-3) for n>=3.
%F From _Colin Barker_, Oct 12 2013: (Start)
%F a(n) = 2*a(n-1) for n>3.
%F G.f.: x*(1 + x + x^2)/(1-2*x). (End)
%F E.g.f.: (7*exp(2*x) - 7 - 6*x - 2*x^2)/8. - _G. C. Greubel_, Jun 05 2019
%e First few rows of A125175 are:
%e 1;
%e 1, 2;
%e 1, 3, 3;
%e 1, 4, 5, 4;
%e ....
%e a(4) = 1 + 4 + 5 + 4 = 14.
%e a(6) = 1 + 6 + 14 + 20 + 9 + 6 = 56 = 7*8 = 7*2^3.
%t Rest@CoefficientList[Series[x*(1+x+x^2)/(1-2*x), {x, 0, 40}], x] (* _Vincenzo Librandi_, Oct 12 2013 *)
%o (PARI) concat([1,3], vector(30, n, 7*2^(n-1))) \\ _G. C. Greubel_, Jun 05 2019
%o (Magma) [1,3] cat [7*2^(n-3): n in [3..40]]; // _G. C. Greubel_, Jun 05 2019
%o (Sage) [1,3]+[7*2^(n-3) for n in (3..40)] # _G. C. Greubel_, Jun 05 2019
%o (GAP) Concatenation([1,3], List([3..40], n-> 7*2^(n-3))) # _G. C. Greubel_, Jun 05 2019
%o (Python) print([7*2**n//8 for n in range(1, 50)]) # _Karl V. Keller, Jr._, May 11 2022
%Y Cf. A125175.
%Y Essentially identical to A005009.
%K nonn,easy
%O 1,2
%A _Gary W. Adamson_, Nov 22 2006
%E More terms from _N. J. A. Sloane_, Dec 15 2007
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