A048479 - OEIS

%I #23 Oct 30 2025 10:32:31

%S 1,9,33,97,257,641,1537,3585,8193,18433,40961,90113,196609,425985,

%T 917505,1966081,4194305,8912897,18874369,39845889,83886081,176160769,

%U 369098753,771751937,1610612737,3355443201,6979321857,14495514625,30064771073,62277025793

%N a(n) = T(7,n), array T given by A048472.

%C n-th difference of a(n), a(n-1), ..., a(0) is (8, 16, 24, ...).

%H Vincenzo Librandi, <a href="/A048479/b048479.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 (5,-8,4).

%F a(n) = 8*n * 2^(n-1) + 1.

%F From _Colin Barker_, Feb 18 2016: (Start)

%F a(n) = 5*a(n-1) - 8*a(n-2) + 4*a(n-3) for n>2.

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

%F a(n) = Sum_{k=0..n+2} Sum_{i=0..n+2} C(n+1,i) - C(k,i). - _Wesley Ivan Hurt_, Sep 21 2017

%F E.g.f.: exp(x)*(1 + 8*x*exp(x)). - _Elmo R. Oliveira_, Oct 30 2025

%t Table[8 n*2^(n - 1) + 1, {n, 0, 29}] (* or *)

%t CoefficientList[Series[(1 + 4 x - 4 x^2)/((1 - x) (1 - 2 x)^2), {x, 0, 29}], x] (* _Michael De Vlieger_, Sep 22 2017 *)

%o (Magma) [8*n * 2^(n-1) + 1: n in [0..30]]; // _Vincenzo Librandi_, Sep 23 2011

%o (PARI) Vec((1+4*x-4*x^2)/((1-x)*(1-2*x)^2) + O(x^40)) \\ _Colin Barker_, Feb 18 2016

%Y Cf. A048472.

%K nonn,easy

%O 0,2

%A _Clark Kimberling_