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 A255687 #42 Aug 18 2025 15:43:51
%S A255687 0,6,25,64,130,230,371,560,804,1110,1485,1936,2470,3094,3815,4640,
%T A255687 5576,6630,7809,9120,10570,12166,13915,15824,17900,20150,22581,25200,
%U A255687 28014,31030,34255,37696,41360,45254,49385,53760,58386,63270,68419,73840,79540,85526
%N A255687 a(n) = n*(n + 1)*(7*n + 11)/6.
%C A255687 This sequence gives the number of triangles of all sizes in (3*n^2+2*n)-polyiamonds in a pentagonal or heptagonal configuration.
%C A255687 Also sum of 2*n*(n+1)*(n+2)/3 triangles oriented in one direction and n*(n+1)^2/2 oriented in the opposite direction.
%H A255687 Colin Barker, <a href="/A255687/b255687.txt">Table of n, a(n) for n = 0..1000</a>
%H A255687 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F A255687 a(n) = (1/2)*(Sum_{j=0..n} (n+1-j)*(3*n-j) + Sum_{j=0..n-1} (n-j)*(3*n+1-3*j)).
%F A255687 From _Colin Barker_, Mar 02 2015: (Start)
%F A255687 a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4).
%F A255687 G.f.: x*(x + 6)/(x - 1)^4. (End)
%F A255687 a(n) = -A007584(-n-1). - _Bruno Berselli_, Mar 02 2015
%F A255687 From _Elmo R. Oliveira_, Aug 18 2025: (Start)
%F A255687 E.g.f.: exp(x)*x*(36 + 39*x + 7*x^2)/6.
%F A255687 a(n) = A212977(2*n). (End)
%p A255687 A255687:=n->n*(n+1)*(7*n+11)/6: seq(A255687(n), n=0..50); # _Wesley Ivan Hurt_, Mar 03 2015
%t A255687 Table[n (n + 1) (7 n + 11)/6, {n, 0, 50}] (* _Bruno Berselli_, Mar 02 2015 *)
%t A255687 LinearRecurrence[{4,-6,4,-1},{0,6,25,64},50] (* _Harvey P. Dale_, Jul 17 2015 *)
%o A255687 (PARI) vector(50, n, n--; n*(n+1)*(7*n+11)/6)
%o A255687 (PARI) concat(0, Vec(x*(x+6)/(x-1)^4 + O(x^100))) \\ _Colin Barker_, Mar 02 2015
%o A255687 (Magma) [n*(n+1)*(7*n+11)/6: n in [0..50]]; // _Bruno Berselli_, Mar 02 2015
%o A255687 (Sage) [n*(n+1)*(7*n+11)/6 for n in (0..50)] # _Bruno Berselli_, Mar 02 2015
%Y A255687 First bisection of A212977.
%Y A255687 Partial sums of A179986.
%Y A255687 Cf. A000292, A006002, A007584, A255211.
%K A255687 nonn,easy
%O A255687 0,2
%A A255687 _Luce ETIENNE_, Mar 02 2015