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 A218327 #9 Jun 02 2025 08:10:17
%S A218327 30,70,364,540,1386,1794,3480,4216,7030,8190,12420,14100,20034,22330,
%T A218327 30256,33264,43470,47286,60060,64780,80410,86130,104904,111720,133926,
%U A218327 141934,167860,177156,207090,217770,252000,264160,302974,316710,360396,375804,424650
%N A218327 Even octagonal pyramidal numbers (A002414).
%H A218327 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (1, 3, -3, -3, 3, 1, -1).
%F A218327 a(n) = a(n-1) + 3*a(n-2) - 3*a(n-3) - 3*a(n-4) + 3*a(n-5) + a(n-6) - a(n-7)
%F A218327 a(n) = 3*a(n-2) - 3*a(n-4) + a(n-6) + 384
%F A218327 a(n) = (4*n-(-1)^n+1)*(4*n-(-1)^n+3)*(4*n-(-1)^n)/8
%F A218327 G. f. 2*x(15+20*x+102*x^2+28*x^3+27*x^4)/((1-x)^4*(1+x)^3)
%e A218327 The sequence of octagonal pyramidal numbers A002414 begins 1, 9, 30, 70, 135, 231, 364, 540, 765, 1045, … As the third even term is 364, then a(3) = 364.
%t A218327 LinearRecurrence[{1,3,-3,-3,3,1,-1},{30,70,364,540,1386,1794,3480},37]
%Y A218327 Cf. A002414, A218326.
%K A218327 nonn
%O A218327 1,1
%A A218327 _Ant King_, Oct 27 2012