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Structured pentagonal icositetrahedral numbers (vertex structure 10).
2

%I #17 Sep 08 2022 08:45:15

%S 1,38,174,472,995,1806,2968,4544,6597,9190,12386,16248,20839,26222,

%T 32460,39616,47753,56934,67222,78680,91371,105358,120704,137472,

%U 155725,175526,196938,220024,244847,271470,299956,330368

%N Structured pentagonal icositetrahedral numbers (vertex structure 10).

%H Vincenzo Librandi, <a href="/A100168/b100168.txt">Table of n, a(n) for n = 1..5000</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) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4); a(1)=1, a(2)=38, a(3)=174, a(4)=472. - _Harvey P. Dale_, Dec 18 2011

%F G.f.: (28*x^2 + 34*x + 1)/(x-1)^4. - _Harvey P. Dale_, Dec 18 2011

%t Table[(63n^3-81n^2+24n)/6,{n,40}]

%t LinearRecurrence[{4,-6,4,-1},{1,38,174,472},40] (* or *) CoefficientList[ Series[(1+34x+28x^2)/(-1+x)^4,{x,0,40}],x](* _Harvey P. Dale_, Dec 18 2011 *)

%o (Magma) [(1/6)*(63*n^3-81*n^2+24*n): n in [1..40]]; // _Vincenzo Librandi_, Jul 26 2011

%Y Cf. A100167 = 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