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 A152773 #56 Feb 16 2025 08:33:09
%S A152773 0,3,21,54,102,165,243,336,444,567,705,858,1026,1209,1407,1620,1848,
%T A152773 2091,2349,2622,2910,3213,3531,3864,4212,4575,4953,5346,5754,6177,
%U A152773 6615,7068,7536,8019,8517,9030,9558,10101,10659,11232,11820,12423,13041,13674,14322,14985
%N A152773 3 times heptagonal numbers: a(n) = 3*n*(5*n-3)/2.
%C A152773 Also the number of 6-cycles in the (n+5)-triangular honeycomb acute knight graph. - _Eric W. Weisstein_, Jun 25 2017
%H A152773 Ivan Panchenko, <a href="/A152773/b152773.txt">Table of n, a(n) for n = 0..1000</a>
%H A152773 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GraphCycle.html">Graph Cycle</a>.
%H A152773 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A152773 a(n) = (15*n^2 - 9*n)/2 = 3*A000566(n).
%F A152773 a(n) = a(n-1) + 15*n - 12 with n > 0, a(0)=0. - _Vincenzo Librandi_, Nov 26 2010
%F A152773 G.f.: 3*x*(1+4*x)/(1-x)^3. - _Bruno Berselli_, Jan 21 2011
%F A152773 a(0)=0, a(1)=3, a(2)=21, a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - _Harvey P. Dale_, May 08 2012
%F A152773 a(n) = n + A226489(n). - _Bruno Berselli_, Jun 11 2013
%F A152773 Sum_{n>=1} 1/a(n) = tan(Pi/10)*Pi/9 - sqrt(5)*log(phi)/9 + 5*log(5)/18, where phi is the golden ratio (A001622). - _Amiram Eldar_, May 20 2023
%F A152773 E.g.f.: 3*exp(x)*x*(2 + 5*x)/2. - _Elmo R. Oliveira_, Dec 24 2024
%t A152773 Table[3 n (5 n - 3)/2, {n, 0, 50}] (* _Harvey P. Dale_, May 08 2012 *)
%t A152773 LinearRecurrence[{3, -3, 1}, {0, 3, 21}, 50] (* _Harvey P. Dale_, May 08 2012 *)
%t A152773 CoefficientList[Series[-((3 x^5 (1 + 4 x))/(-1 + x)^3), {x, 0, 20}], x] (* _Eric W. Weisstein_, Jun 25 2017 *)
%o A152773 (PARI) a(n)=3*n*(5*n-3)/2 \\ _Charles R Greathouse IV_, Sep 24 2015
%Y A152773 Cf. A000566, A001622, A135706, A226489.
%Y A152773 3 times n-gonal numbers: A045943, A033428, A062741, A094159, A152751, A152759, A152767, A153783, A153448, A153875.
%Y A152773 Cf. numbers of the form n*(n*k - k + 6)/2, this sequence is the case k=15: see Comments lines of A226492.
%Y A152773 Cf. A002378 (3-cycles in triangular honeycomb acute knight graph), A045943 (4-cycles), A028896 (5-cycles).
%K A152773 nonn,easy
%O A152773 0,2
%A A152773 _Omar E. Pol_, Dec 13 2008