A081588 Fourth row of the Pascal-(1,4,1) array A081579.
1, 16, 106, 396, 1011, 2076, 3716, 6056, 9221, 13336, 18526, 24916, 32631, 41796, 52536, 64976, 79241, 95456, 113746, 134236, 157051, 182316, 210156, 240696, 274061, 310376, 349766, 392356, 438271, 487636, 540576, 597216, 657681, 722096, 790586, 863276, 940291
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).
Programs
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Magma
[(6+115*n-150*n^2+125*n^3)/6: n in [0..40]]; // Vincenzo Librandi, Aug 09 2013
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Mathematica
CoefficientList[Series[(1 + 4 x)^3 / (1 - x)^4, {x, 0, 40}], x] (* Vincenzo Librandi, Aug 09 2013 *)
Formula
a(n) = (6 + 115*n - 150*n^2 + 125*n^3)/6.
G.f.: (1+4*x)^3/(1-x)^4.
From Elmo R. Oliveira, Jun 06 2025: (Start)
E.g.f.: exp(x)*(6 + 90*x + 225*x^2 + 125*x^3)/6.
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4). (End)