OFFSET
0,2
COMMENTS
The binomial transform is in A126184.
An elephant sequence, see A175654 and A175655. There are 24 A[5] vectors, with decimal values between 7 and 448, that lead for the corner squares to this sequence. Its companion sequence for the central square is A175656. Furthermore there are 36 A[5] vectors, with decimal values between 15 and 480, that lead for the central square to four times this sequence for n >= -1. Its companion sequence for the corner squares is A059570. - Johannes W. Meijer, Aug 15 2010
a(n) is also the number of runs of weakly increasing parts in all compositions of n+1. a(2) = 5: (111), (12), (2)(1), (3). - Alois P. Heinz, Apr 30 2017
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (3,0,-4)
FORMULA
MATHEMATICA
Table[(3n 2^n+2^(n+4)+2(-1)^n)/18, {n, 0, 40}] (* or *)
CoefficientList[Series[(1-x-x^2)/((1+x)(1-2x)^2), {x, 0, 40}], x] (* Harvey P. Dale, Mar 28 2011 *)
PROG
(Magma) [(3*n*2^n+2^(n+4)+2*(-1)^n)/18: n in [0..40]]; // Vincenzo Librandi, Aug 04 2011
(PARI) a(n)=(3*n*2^n+2^(n+4)+2*(-1)^n)/18 \\ Charles R Greathouse IV, Oct 07 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Paul Curtz, Feb 04 2010
EXTENSIONS
Definition replaced by explicit formula by R. J. Mathar, Feb 11 2010
STATUS
approved