# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a100187 Showing 1-1 of 1 %I A100187 #24 Sep 08 2022 08:45:15 %S A100187 1,18,77,204,425,766,1253,1912,2769,3850,5181,6788,8697,10934,13525, %T A100187 16496,19873,23682,27949,32700,37961,43758,50117,57064,64625,72826, %U A100187 81693,91252,101529,112550,124341,136928 %N A100187 Structured octagonal anti-diamond numbers (vertex structure 7). %H A100187 Vincenzo Librandi, Table of n, a(n) for n = 1..10000 %H A100187 Index entries for linear recurrences with constant coefficients, signature (4, -6, 4, -1). %F A100187 a(n) = (1/6)*(26*n^3 - 30*n^2 + 10*n). %F A100187 G.f.: x*(1 + 14*x + 11*x^2)/(1-x)^4. - _Colin Barker_, Jan 19 2012 %F A100187 a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4); a(1)=1, a(2)=18, a(3)=77, a(4)=204. - _Harvey P. Dale_, Dec 24 2012 %F A100187 E.g.f.: (3*x + 24*x^2 + 13*x^3)*exp(x)/3. - _G. C. Greubel_, Nov 08 2018 %t A100187 Table[(26n^3-30n^2+10n)/6,{n,40}] (* or *) LinearRecurrence[{4,-6,4,-1},{1,18,77,204},40] (* _Harvey P. Dale_, Dec 24 2012 *) %o A100187 (Magma) [(1/6)*(26*n^3-30*n^2+10*n): n in [1..40]]; // _Vincenzo Librandi_, Aug 18 2011 %o A100187 (PARI) vector(40, n, (13*n^3 -15*n^2 +5*n)/3) \\ _G. C. Greubel_, Nov 08 2018 %Y A100187 Cf. A063523 = alternate vertex; A100188 = structured anti-diamonds; A100145 for more on structured numbers. %K A100187 nonn,easy %O A100187 1,2 %A A100187 James A. Record (james.record(AT)gmail.com), Nov 07 2004 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE