A141478 a(n) = binomial(n+2,3)*4^3.
64, 256, 640, 1280, 2240, 3584, 5376, 7680, 10560, 14080, 18304, 23296, 29120, 35840, 43520, 52224, 62016, 72960, 85120, 98560, 113344, 129536, 147200, 166400, 187200, 209664, 233856, 259840, 287680, 317440, 349184, 382976, 418880, 456960, 497280, 539904, 584896
Offset: 1
Links
- Vincenzo Librandi, Table of n, a(n) for n = 1..1000
- Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).
Programs
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Magma
[Binomial(n+2,3)*4^3: n in [1..34]]; // Bruno Berselli, Apr 07 2011
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Magma
I:=[64, 256, 640, 1280]; [n le 4 select I[n] else 4*Self(n-1)-6*Self(n-2)+4*Self(n-3)-Self(n-4): n in [1..50]]; // Vincenzo Librandi, Jun 29 2012
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Maple
seq(binomial(n+2,3)*4^3, n=1..36);
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Mathematica
CoefficientList[Series[64/(1-x)^4,{x,0,40}],x] (* Vincenzo Librandi, Jun 29 2012 *)
Formula
G.f.: 64*x/(1-x)^4.
a(n) = 32*n*(n+1)*(n+2)/3 = 64*A000292(n).
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4). - Vincenzo Librandi, Jun 29 2012
From Amiram Eldar, Aug 29 2022: (Start)
Sum_{n>=1} 1/a(n) = 3/128.
Sum_{n>=1} (-1)^(n+1)/a(n) = 3*log(2)/16 - 15/128. (End)
From Elmo R. Oliveira, Aug 19 2025: (Start)
E.g.f.: 32*x*(6 + 6*x + x^2)*exp(x)/3.
a(n) = 16*A210440(n). (End)
Extensions
Offset adapted to the g.f. by Bruno Berselli, Apr 07 2011