A179904 - OEIS

%I #34 Jul 14 2024 20:00:40

%S 1,3,7,16,32,57,93,142,206,287,387,508,652,821,1017,1242,1498,1787,

%T 2111,2472,2872,3313,3797,4326,4902,5527,6203,6932,7716,8557,9457,

%U 10418,11442,12531,13687,14912,16208,17577,19021,20542,22142,23823,25587

%N a(n) = A056520(n)+1 for n>0, a(0)=1.

%C Original name: (1,3,5,7,9,..) = A005408 convolved with (1,0,2,3,4,..) = 1 followed by A087156.

%H Vincenzo Librandi, <a href="/A179904/b179904.txt">Table of n, a(n) for n = 0..10000</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).

%F From _Bruno Berselli_, Aug 26 2011: (Start)

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

%F a(n) = (1/6)*(2*n^3 + 3*n^2 + n + 12) for n>0, a(0)=1. (End)

%F a(n) = A153056(n) for n > 0. - _Georg Fischer_, Oct 24 2018

%e a(3) = 16 = 1 + A056520(3) = (1 + 15).

%e a(4) = 32 = (9, 7, 5, 3, 1) dot (1, 0, 2, 3, 4) = (9 + 0 + 10 + 9 + 4).

%t LinearRecurrence[{4,-6,4,-1},{1,3,7,16,32},50] (* _Harvey P. Dale_, Apr 25 2020 *)

%Y Cf. A000330, A056520, A153056, A153057, A153058.

%K nonn,easy

%O 0,2

%A _Gary W. Adamson_, Jul 31 2010

%E More terms and a(20) added by _Bruno Berselli_, Aug 26 2011