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 A152767 #45 Aug 13 2025 09:52:07
%S A152767 0,3,30,81,156,255,378,525,696,891,1110,1353,1620,1911,2226,2565,2928,
%T A152767 3315,3726,4161,4620,5103,5610,6141,6696,7275,7878,8505,9156,9831,
%U A152767 10530,11253,12000,12771,13566,14385,15228,16095,16986,17901,18840,19803,20790,21801
%N A152767 3 times 10-gonal (or decagonal) numbers: a(n) = 3*n*(4*n-3).
%C A152767 3*A172078(n) = n*a(n) - Sum_{k=0..n-1} a(k). - _Bruno Berselli_, Dec 12 2010
%D A152767 "Supplemento al Periodico di Matematica", Raffaello Giusti Editore (Livorno), Jan. 1910 p. 47 (Problem 1052).
%H A152767 Harvey P. Dale, <a href="/A152767/b152767.txt">Table of n, a(n) for n = 0..1000</a>
%H A152767 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A152767 a(n) = 12*n^2 - 9*n = 3*A001107(n).
%F A152767 a(n) = a(n-1) + 24*n - 21, n > 0. - _Vincenzo Librandi_, Nov 26 2010
%F A152767 a(n) = Sum_{k=0..n-1} A001539(k) - Sum_{k=0..n-1} 4*A002939(k) if n > 0 (see References, Problem 1052). - _Bruno Berselli_, Dec 08 2010 - Jan 21 2011
%F A152767 G.f.: -3*x*(1+7*x)/(x-1)^3.
%F A152767 a(0)=0, a(1)=3, a(2)=30, a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - _Harvey P. Dale_, May 26 2012
%F A152767 From _Elmo R. Oliveira_, Dec 15 2024: (Start)
%F A152767 E.g.f.: 3*exp(x)*x*(1 + 4*x).
%F A152767 a(n) = A153794(n) - n. (End)
%e A152767 For n=8, a(8) = (1*3 + 5*7 + 9*11 +..+ 29*31) - (2*4 + 6*8 + 10*12 +..+ 26*28) = 696 (see Problem 1052 in References). - _Bruno Berselli_, Dec 12 2010
%t A152767 Table[3n(4n-3),{n,0,40}] (* _Harvey P. Dale_, May 26 2012 *)
%o A152767 (PARI) a(n)=3*n*(4*n-3) \\ _Charles R Greathouse IV_, Sep 28 2015
%Y A152767 Cf. A001107, A001539, A002939, A139271, A153794, A172078.
%Y A152767 3 times n-gonal numbers: A045943, A033428, A062741, A094159, A152773, A152751, A152759, A153783, A153448, A153875.
%Y A152767 Cf. numbers of the form n*(n*k - k + 6)/2, this sequence is the case k=24: see Comments lines of A226492.
%K A152767 nonn,easy
%O A152767 0,2
%A A152767 _Omar E. Pol_, Dec 15 2008