A100168 Structured pentagonal icositetrahedral numbers (vertex structure 10).
1, 38, 174, 472, 995, 1806, 2968, 4544, 6597, 9190, 12386, 16248, 20839, 26222, 32460, 39616, 47753, 56934, 67222, 78680, 91371, 105358, 120704, 137472, 155725, 175526, 196938, 220024, 244847, 271470, 299956, 330368
Offset: 1
Links
- Vincenzo Librandi, Table of n, a(n) for n = 1..5000
- Index entries for linear recurrences with constant coefficients, signature (4, -6, 4, -1).
Programs
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Magma
[(1/6)*(63*n^3-81*n^2+24*n): n in [1..40]]; // Vincenzo Librandi, Jul 26 2011
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Mathematica
Table[(63n^3-81n^2+24n)/6,{n,40}] 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 *)
Formula
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
G.f.: (28*x^2 + 34*x + 1)/(x-1)^4. - Harvey P. Dale, Dec 18 2011