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Structured triakis octahedral numbers (vertex structure 4).
3

%I #18 Sep 08 2022 08:45:15

%S 1,14,60,160,335,606,994,1520,2205,3070,4136,5424,6955,8750,10830,

%T 13216,15929,18990,22420,26240,30471,35134,40250,45840,51925,58526,

%U 65664,73360,81635,90510,100006,110144

%N Structured triakis octahedral numbers (vertex structure 4).

%H Vincenzo Librandi, <a href="/A100171/b100171.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)*(21*n^3-27*n^2+12*n).

%F a(0)=1, a(1)=14, a(2)=60, a(3)=160, a(n)=4*a(n-1)-6*a(n-2)+4*a(n-3)-a(n-4). - _Harvey P. Dale_, Jun 28 2011

%F G.f.: (10*x^2+10*x+1)/(x-1)^4. - _Harvey P. Dale_, Jun 28 2011

%t Table[(21n^3-27n^2+12n)/6,{n,40}] (* or *) LinearRecurrence[ {4,-6,4,-1},{1,14,60,160},40] (* _Harvey P. Dale_, Jun 28 2011 *)

%o (Magma) [(1/6)*(21*n^3-27*n^2+12*n): n in [1..40]]; // _Vincenzo Librandi_, Jul 27 2011

%Y Cf. A100157 = alternate vertex; A100145 for more on structured numbers.

%K easy,nonn

%O 1,2

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