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
KEYWORD
nonn,easy
AUTHOR
Mohammad K. Azarian, May 01 2007
STATUS
approved