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 A270694 #23 Sep 08 2022 08:46:16
%S A270694 0,-1,8,-23,51,-94,157,-242,354,-495,670,-881,1133,-1428,1771,-2164,
%T A270694 2612,-3117,3684,-4315,5015,-5786,6633,-7558,8566,-9659,10842,-12117,
%U A270694 13489,-14960,16535,-18216,20008,-21913,23936,-26079,28347,-30742,33269
%N A270694 Alternating sum of centered heptagonal pyramidal numbers.
%C A270694 More generally, the ordinary generating function for the alternating sum of centered k-gonal pyramidal numbers is -x*(1 - (k - 2)*x + x^2)/((1 - x)*(1 + x)^4).
%H A270694 Ilya Gutkovskiy, <a href="/A270694/b270694.txt">Table of n, a(n) for n = 0..500</a>
%H A270694 OEIS Wiki, <a href="http://oeis.org/wiki/Centered_pyramidal_numbers">Centered pyramidal numbers</a>
%H A270694 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (-3,-2,2,3,1).
%F A270694 G.f.: -x*(1 - 5*x + x^2)/((1 - x)*(1 + x)^4).
%F A270694 a(n) = -3*a(n-1) - 2*a(n-2) + 2*a(n-3) + 3*a(n-4) + a(n-5).
%F A270694 a(n) = ((-1)^n*(2*n + 1)*(14*n^2 + 14*n - 9) + 9)/48.
%F A270694 E.g.f.: (1/48)*(9*exp(x) - (9 + 66*x - 126*x^2 + 28*x^3)*exp(-x)). - _G. C. Greubel_, Mar 28 2016
%p A270694 A270694:= n-> ((-1)^n*(2*n+1)*(14*n^2+14*n-9) + 9)/48; seq(A270694(n), n=0..40); # _G. C. Greubel_, Apr 02 2021
%t A270694 LinearRecurrence[{-3, -2, 2, 3, 1}, {0, -1, 8, -23, 51}, 39]
%t A270694 Table[((-1)^n (2 n + 1) (14 n^2 + 14 n - 9) + 9)/48, {n, 0, 38}]
%o A270694 (PARI) my(x='x+O('x^50)); concat(0, Vec(-x*(1-5*x+x^2)/((1-x)*(1+x)^4))) \\ _Altug Alkan_, Mar 21 2016
%o A270694 (Magma) [((-1)^n*(2*n + 1)*(14*n^2 + 14*n - 9) + 9)/48 : n in [0..40]]; // _Wesley Ivan Hurt_, Mar 21 2016
%o A270694 (Sage) [((-1)^n*(2*n+1)*(14*n^2+14*n-9) +9)/48 for n in (0..40)] # _G. C. Greubel_, Apr 02 2021
%Y A270694 Cf. A004126 (centered heptagonal pyramidal numbers).
%Y A270694 Cf. A000330, A006323 (partial sums of centered heptagonal pyramidal numbers), A019298, A232599.
%K A270694 easy,sign
%O A270694 0,3
%A A270694 _Ilya Gutkovskiy_, Mar 21 2016