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 A190718 #21 Aug 01 2023 17:52:58
%S A190718 1,1,1,1,4,4,4,4,10,10,10,10,20,20,20,20,35,35,35,35,56,56,56,56,84,
%T A190718 84,84,84,120,120,120,120,165,165,165,165,220,220,220,220,286,286,286,
%U A190718 286,364,364,364,364,455,455,455,455
%N A190718 Quadruplicated tetrahedral numbers A000292.
%C A190718 The Gi1 triangle sums, for the definitions of these and other triangle sums see A180662, of the triangle A159797 are linear sums of shifted versions of the quadruplicated tetrahedral numbers A000292, i.e., Gi1(n) = a(n-1) + a(n-2) + a(n-3) + 2*a(n-4) + a(n-8).
%C A190718 The Gi1 and Gi2 triangle sums of the Connell sequence A001614 as a triangle are also linear sums of shifted versions of the sequence given above.
%H A190718 <a href="/index/Rec#order_13">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,3,-3,0,0,-3,3,0,0,1,-1).
%F A190718 a(n) = binomial(floor(n/4)+3,3).
%F A190718 a(n-3) + a(n-2) + a(n-1) + a(n) = A144678(n).
%F A190718 a(n) = +a(n-1) +3*a(n-4) -3*a(n-5) -3*a(n-8) +3*a(n-9) +a(n-12) -a(n-13).
%F A190718 G.f.: 1 / ( (1+x)^3*(1+x^2)^3*(x-1)^4 ).
%F A190718 Sum_{n>=0} 1/a(n) = 6. - _Amiram Eldar_, Aug 18 2022
%p A190718 A190718:= proc(n) binomial(floor(n/4)+3,3) end:
%p A190718 seq(A190718(n),n=0..52);
%t A190718 LinearRecurrence[{1,0,0,3,-3,0,0,-3,3,0,0,1,-1},{1,1,1,1,4,4,4,4,10,10,10,10,20},60] (* _Harvey P. Dale_, Oct 20 2012 *)
%Y A190718 Cf. A000292 (tetrahedral numbers), A058187 (duplicated), A190717 (triplicated).
%K A190718 nonn,easy
%O A190718 0,5
%A A190718 _Johannes W. Meijer_, May 18 2011