|
|
A172481
|
|
a(n) = (3*n*2^n+2^(n+4)+2*(-1)^n)/18.
|
|
8
|
|
|
1, 2, 5, 11, 25, 55, 121, 263, 569, 1223, 2617, 5575, 11833, 25031, 52793, 111047, 233017, 487879, 1019449, 2126279, 4427321, 9204167, 19107385, 39612871, 82021945, 169636295, 350457401, 723284423, 1491308089, 3072094663, 6323146297, 13004206535, 26724240953
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
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
|
|
|
FORMULA
|
G.f.: (1-x-x^2)/((1+x)*(1-2*x)^2).
|
|
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
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
EXTENSIONS
|
Definition replaced by explicit formula by R. J. Mathar, Feb 11 2010
|
|
STATUS
|
approved
|
|
|
|