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 A341043 #20 Sep 02 2025 04:23:36 %S A341043 1,35,189,559,1241,2331,3925,6119,9009,12691,17261,22815,29449,37259, %T A341043 46341,56791,68705,82179,97309,114191,132921,153595,176309,201159, %U A341043 228241,257651,289485,323839,360809,400491,442981,488375,536769,588259,642941,700911,762265 %N A341043 a(n) = 16*n^3 - 36*n^2 + 30*n - 9. %C A341043 The n-th term of A155883 (hexagonal bifrustum numbers) has a hexagonal pyramid of [n - 1] set on each of its two hexagonal faces. %C A341043 The digital roots run recursively 1, 8, 9. %C A341043 The sum of the first n consecutive terms is the square of the n-th hexagonal number. %H A341043 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1). %F A341043 a(n) = 16*n^3 - 36*n^2 + 30*n - 9. %F A341043 a(n) = A155883(n) + 2*A000578(n-1). %F A341043 G.f.: x*(1 + 31*x + 55*x^2 + 9*x^3)/(1 - x)^4. - _Stefano Spezia_, Feb 04 2021 %F A341043 From _Elmo R. Oliveira_, Sep 01 2025: (Start) %F A341043 E.g.f.: 9 + exp(x)*(-9 + 10*x + 12*x^2 + 16*x^3). %F A341043 a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4). (End) %e A341043 For n = 3 the solution is 173 + 8 + 8 = 189. %o A341043 (PARI) Vec(x*(9*x^3+55*x^2+31*x+1)/(x-1)^4 + O(x^38)) \\ _Elmo R. Oliveira_, Sep 01 2025 %Y A341043 Cf. A000384, A000578, A155883. %K A341043 nonn,easy,changed %O A341043 1,2 %A A341043 _David Z Crookes_, Feb 03 2021 %E A341043 More terms from _Elmo R. Oliveira_, Sep 01 2025