A192811 - OEIS

%I #37 Sep 22 2025 16:01:06

%S 0,0,1,7,37,183,893,4351,21205,103367,503917,2456655,11976517,

%T 58387095,284644701,1387679903,6765119669,32980836455,160785858381,

%U 783851928559,3821379890981,18629722961207,90822317465149,442770585849407,2158564075053717,10523280034904327

%N a(n) = A192809(n)/2.

%H G. C. Greubel, <a href="/A192811/b192811.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 (7,-12,8).

%F a(n) = 7*a(n-1) - 12*a(n-2) + 8*a(n-3).

%F G.f.: x^2/(1-7*x+12*x^2-8*x^3). - _Colin Barker_, Jul 26 2012

%F a(n) = Sum_{k=0..floor((3*n-6)/2)} binomial(3*n-4-2*k, k)*2^k. - _Taras Goy_, Sep 15 2025

%t (* See A192808. *)

%t LinearRecurrence[{7,-12,8},{0,0,1},30] (* _Harvey P. Dale_, Dec 06 2018 *)

%o (PARI) my(x='x+O('x^30)); concat([0,0], Vec(x^2/(1-7*x+12*x^2-8*x^3))) \\ _G. C. Greubel_, Jan 03 2019

%o (Magma) m:=30; R<x>:=PowerSeriesRing(Integers(), m); [0,0] cat Coefficients(R!( x^2/(1-7*x+12*x^2-8*x^3) )); // _G. C. Greubel_, Jan 03 2019

%o (SageMath) (x^2/(1-7*x+12*x^2-8*x^3)).series(x, 30).coefficients(x, sparse=False) # _G. C. Greubel_, Jan 03 2019

%o (GAP) a:=[0,0,1];; for n in [4..25] do a[n]:=7*a[n-1]-12*a[n-2]+8*a[n-3]; od; Print(a); # _Muniru A Asiru_, Jan 03 2019

%Y Cf. A192232, A192744, A192809.

%K nonn,easy

%O 0,4

%A _Clark Kimberling_, Jul 10 2011

%E Name corrected by _Colin Barker_, Jul 26 2012