This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A193744 #23 May 25 2025 20:43:06
%S A193744 3,3,5,8,10,15,20,27,37,49,66,88,117,156,207,275,365,484,642,851,1128,
%T A193744 1495,1981,2625,3478,4608,6105,8088,10715,14195,18805,24912,33002,
%U A193744 43719,57916,76723,101637,134641,178362,236280,313005,414644,549287,727651,963933,1276940,1691586
%N A193744 Partial sum of Perrin numbers.
%H A193744 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,0,-1).
%F A193744 a(n) = Perrin(n+5)-2.
%F A193744 a(n) = r1^(n+5)+r2^(n+5)+r3^(n+5)-2, where r1, r2, r3 are the three roots of x^3-x-1 = 0.
%F A193744 G.f.: (3 - x^2)/(1 - x^2 - x^3)/(1-x) = (3 - x^2) / (1 - x - x^2 + x^4). a(n) = a(n-1) + a(n-2) - a(n-4) for n > 2. - _Franklin T. Adams-Watters_, Aug 05 2011
%e A193744 For n=2, a(2)=Perrin(0)+Perrin(1)+Perrin(2)=3+0+2=5.
%p A193744 perrin[0]:=3: perrin[1]:=0: perrin[2]:=2: a[0]:=3: a[1]:=3: a[2]:=5: for n from 0 to 100 do perrin[n]:=perrin[n-2]+perrin[n-3]: a[n]:=a[n-1]+perrin[n]: end do;
%t A193744 LinearRecurrence[{0, 1, 1}, {3, 0, 2}, {6, 52}] - 2 (* _Alonso del Arte_, Aug 05 2011, based on Harvey P. Dale's program for A001608 *)
%t A193744 LinearRecurrence[{1, 1, 0, -1},{3, 3, 5, 8},47] (* _Ray Chandler_, Aug 03 2015 *)
%Y A193744 Cf. A001608.
%K A193744 nonn,easy
%O A193744 0,1
%A A193744 _Francesco Daddi_, Aug 04 2011