A081590 Fourth row of Pascal-(1,5,1) array A081580.
1, 19, 145, 595, 1585, 3331, 6049, 9955, 15265, 22195, 30961, 41779, 54865, 70435, 88705, 109891, 134209, 161875, 193105, 228115, 267121, 310339, 357985, 410275, 467425, 529651, 597169, 670195, 748945, 833635, 924481, 1021699, 1125505, 1236115, 1353745, 1478611
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..10000
- Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).
Programs
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Magma
[1+36*n-54*n^2+36*n^3: n in [0..40]]; // Vincenzo Librandi, Sep 07 2011
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Mathematica
Table[36n^3-54n^2+36n+1,{n,0,50}] (* or *) LinearRecurrence[{4,-6,4,-1},{1,19,145,595},50] (* Harvey P. Dale, Sep 07 2011 *)
Formula
a(n) = 1 + 36*n - 54*n^2 + 36*n^3.
G.f.: (1+5*x)^3/(1-x)^4.
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4); a(0)=1, a(1)=19, a(2)=145, a(3)=595. - Harvey P. Dale, Sep 07 2011
E.g.f.: exp(x)*(1 + 18*x + 54*x^2 + 36*x^3). - Elmo R. Oliveira, Jun 06 2025