A131833 a(n) = 2^(n+1) - 1 + 3*n.
1, 6, 13, 24, 43, 78, 145, 276, 535, 1050, 2077, 4128, 8227, 16422, 32809, 65580, 131119, 262194, 524341, 1048632, 2097211, 4194366, 8388673, 16777284, 33554503, 67108938, 134217805, 268435536, 536870995, 1073741910, 2147483737, 4294967388, 8589934687, 17179869282
Offset: 0
Examples
a(3) = 24 = sum of row 3 terms of triangle A131832: (7 + 5 + 5 + 7). a(3) = 24 = (1, 3, 3, 1) dot (1, 5, 2, 2) = (1 + 15 + 6 + 2).
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (4,-5,2).
Crossrefs
Row sums of triangle A131832.
Programs
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Magma
I:=[1, 6, 13]; [n le 3 select I[n] else 4*Self(n-1)-5*Self(n-2)+2*Self(n-3): n in [1..40]]; // Vincenzo Librandi, Jul 05 2012
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Mathematica
CoefficientList[Series[(-1-2*x+6*x^2)/((2*x-1)*(x-1)^2),{x,0,40}],x] (* Vincenzo Librandi, Jul 05 2012 *) Table[2^(n+1)-1+3n,{n,0,30}] (* or *) LinearRecurrence[{4,-5,2},{1,6,13},40] (* Harvey P. Dale, Nov 06 2012 *)
Formula
G.f.: (-1 - 2*x + 6*x^2)/((2*x - 1)*(x - 1)^2). - R. J. Mathar, Apr 04 2012
a(n) = 4*a(n-1) - 5*a(n-2) + 2*a(n-3). - Vincenzo Librandi, Jul 05 2012
E.g.f.: exp(x)*(2*exp(x) - 1 + 3*x). - Stefano Spezia, Mar 29 2023
Extensions
New definition by R. J. Mathar, Apr 04 2012
Comments