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 A006597 #47 Aug 06 2025 17:09:13
%S A006597 0,1,14,54,136,275,486,784,1184,1701,2350,3146,4104,5239,6566,8100,
%T A006597 9856,11849,14094,16606,19400,22491,25894,29624,33696,38125,42926,
%U A006597 48114,53704,59711,66150,73036,80384,88209,96526,105350,114696,124579,135014,146016,157600
%N A006597 a(n) = n^2*(5*n-3)/2.
%C A006597 Structured heptagonal prism numbers. - James A. Record (james.record(AT)gmail.com), Nov 07 2004
%C A006597 Apart from 0, partial sums of A220083. - _Bruno Berselli_, Dec 11 2012
%D A006597 W. A. Whitworth, DCC Exercises in Choice and Chance, Stechert, NY, 1945, p. 29.
%H A006597 Vincenzo Librandi, <a href="/A006597/b006597.txt">Table of n, a(n) for n = 0..10000</a>
%H A006597 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F A006597 a(n) = (1/6)*(15*n^3 - 9*n^2). - James A. Record (james.record(AT)gmail.com), Nov 07 2004
%F A006597 G.f.: x*(1+10*x+4*x^2)/(1-x)^4. - _Colin Barker_, Jun 08 2012
%F A006597 a(n) = Sum_{i=0..n-1} n*(5*i+1) for n>0. - _Bruno Berselli_, Sep 08 2015
%F A006597 Sum_{n>=1} 1/a(n) = 1.1080093773051638036... = (sqrt(5*(5 - 2*sqrt(5)))*Pi - Pi^2 - 5*sqrt(5)*arccoth(sqrt(5)) + (25*log(5))/2)/9. - _Vaclav Kotesovec_, Oct 04 2016
%F A006597 From _Elmo R. Oliveira_, Aug 06 2025: (Start)
%F A006597 E.g.f.: exp(x)*x*(2 + 12*x + 5*x^2)/2.
%F A006597 a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4).
%F A006597 a(n) = A006592(n)/4. (End)
%p A006597 A006597:=n->n^2*(5*n-3)/2; seq(A006597(n), n=0..40); # _Wesley Ivan Hurt_, Mar 11 2014
%t A006597 Table[n^2*(5*n-3)/2, {n, 0, 40}] (* _Wesley Ivan Hurt_, Mar 11 2014 *)
%o A006597 (Magma) [n^2*(5*n-3)/2: n in [0..40]]; // _Vincenzo Librandi_, Jul 20 2011
%o A006597 (PARI) a(n)=n^2*(5*n-3)/2; \\ _Joerg Arndt_, Jul 20 2011
%Y A006597 Cf. A100177 - structured prisms; A100145 for more on structured numbers.
%Y A006597 Cf. similar sequences, with the formula (k*n - k + 2)*n^2/2, listed in A262000.
%Y A006597 Cf. A006592, A220083.
%K A006597 nonn,easy
%O A006597 0,3
%A A006597 _N. J. A. Sloane_
%E A006597 Name corrected by _Arkadiusz Wesolowski_, Jul 20 2011