A129002 a(n) = (n^3 + n^2)*2^n.

4, 48, 288, 1280, 4800, 16128, 50176, 147456, 414720, 1126400, 2973696, 7667712, 19382272, 48168960, 117964800, 285212672, 681836544, 1613758464, 3785359360, 8808038400, 20346568704, 46690992128, 106501767168, 241591910400

Offset

1,1

Comments

Number of paths along four vertices contained within the n+1 dimensional hypercube graph. - Ben Eck, Mar 30 2022

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (8,-24,32,-16).

Formula

G.f.: 4x*(1+4*x)/(1-2*x)^4. - Vincenzo Librandi, Feb 12 2013

a(n) = 8*a(n-1) - 24*a(n-2) + 32*a(n-3) - 16*a(n-4). - Vincenzo Librandi, Feb 12 2013

Sum_{n>=1} 1/a(n) = Pi^2/12 - 1 + log(2) - log(2)^2/2. - Amiram Eldar, Aug 05 2020

Mathematica

CoefficientList[Series[4 (1 + 4 x)/(1 - 2 x)^4, {x, 0, 30}], x] (* Vincenzo Librandi, Feb 12 2013 *)
LinearRecurrence[{8, -24, 32, -16}, {4, 48, 288, 1280}, 30] (* Harvey P. Dale, Aug 21 2021 *)

Prog

(Magma) [(n^3+n^2)*2^n: n in [1..25]]; /* or */ I:=[4, 48, 288, 1280]; [n le 4 select I[n] else 8*Self(n-1)-24*Self(n-2)+32*Self(n-3)-16*Self(n-4): n in [1..25]]; // Vincenzo Librandi, Feb 12 2013
(PARI) a(n)=(n^3+n^2)<<n \\ Charles R Greathouse IV, Oct 07 2015

Crossrefs

Cf. A128796, A036289.

Sequence in context: A292074 A274729 A217153 * A291623 A144704 A091904

Adjacent sequences: A128999 A129000 A129001 * A129003 A129004 A129005

Keyword

nonn,easy

Author

Mohammad K. Azarian, May 01 2007

Status

approved