%I #24 Sep 08 2022 08:45:15

%S 1,18,77,204,425,766,1253,1912,2769,3850,5181,6788,8697,10934,13525,

%T 16496,19873,23682,27949,32700,37961,43758,50117,57064,64625,72826,

%U 81693,91252,101529,112550,124341,136928

%N Structured octagonal anti-diamond numbers (vertex structure 7).

%H Vincenzo Librandi, <a href="/A100187/b100187.txt">Table of n, a(n) for n = 1..10000</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4, -6, 4, -1).

%F a(n) = (1/6)*(26*n^3 - 30*n^2 + 10*n).

%F G.f.: x*(1 + 14*x + 11*x^2)/(1-x)^4. - _Colin Barker_, Jan 19 2012

%F 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 E.g.f.: (3*x + 24*x^2 + 13*x^3)*exp(x)/3. - _G. C. Greubel_, Nov 08 2018

%t 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 (Magma) [(1/6)*(26*n^3-30*n^2+10*n): n in [1..40]]; // _Vincenzo Librandi_, Aug 18 2011

%o (PARI) vector(40, n, (13*n^3 -15*n^2 +5*n)/3) \\ _G. C. Greubel_, Nov 08 2018

%Y Cf. A063523 = alternate vertex; A100188 = structured anti-diamonds; A100145 for more on structured numbers.

%K nonn,easy

%O 1,2

%A James A. Record (james.record(AT)gmail.com), Nov 07 2004