A131066 - OEIS

%I #31 Sep 08 2022 08:45:30

%S 1,2,9,28,71,162,349,728,1491,3022,6089,12228,24511,49082,98229,

%T 196528,393131,786342,1572769,3145628,6291351,12582802,25165709,

%U 50331528,100663171,201326462,402653049,805306228,1610612591,3221225322

%N Binomial transform of [1, 1, 6, 6, 6, ...].

%C Row sums of triangle A131065. - _Emeric Deutsch_, Jun 20 2007

%H Muniru A Asiru, <a href="/A131066/b131066.txt">Table of n, a(n) for n = 0..2000</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (4,-5,2).

%F From _Emeric Deutsch_, Jun 20 2007: (Start)

%F a(n) = 6*2^n - 5*(n + 1).

%F G.f.: (1 - 2*x + 6*x^2)/((1-2*x)*(1-x)^2). (End)

%F E.g.f.: 6*exp(2*x) - 5*(1 + x)*exp(x). - _G. C. Greubel_, Mar 12 2020

%F a(n) = 2*a(n - 1) + 5*n - 5. - _Kritsada Moomuang_, Jul 03 2020

%F a(n) = 4*a(n-1) - 5*a(n-2) + 2*a(n-3). - _Wesley Ivan Hurt_, Jul 10 2020

%e a(3) = 28 = sum of row 4 of triangle A131065: (1 + 13 + 13 + 1).

%e a(3) = 28 = (1, 3, 3, 1) dot (1, 1, 6, 6) = (1 + 3 + 18 + 6).

%p a := proc (n) options operator, arrow; 6*2^n-5*n-5 end proc: seq(a(n), n = 0 .. 30); # _Emeric Deutsch_, Jun 20 2007

%t Table[6*2^n -5*(n+1), {n,0,30}] (* _G. C. Greubel_, Mar 12 2020 *)

%o (GAP) Print(List([0..30],n->6*2^n-5*n-5)); # _Muniru A Asiru_, Feb 21 2019

%o (Magma) [6*2^n -5*(n+1): n in [0..30]]; // _G. C. Greubel_, Mar 12 2020

%o (Sage) [6*2^n -5*(n+1) for n in (0..30)] # _G. C. Greubel_, Mar 12 2020

%Y Cf. A109128, A123203, A131060, A131061, A131063, A131064, A131065, A131067, A131068.

%K nonn

%O 0,2

%A _Gary W. Adamson_, Jun 13 2007

%E Corrected and extended by _Emeric Deutsch_, Jun 20 2007