|
| |
|
|
A125816
|
|
a(n)=((1+sqrt(13))^n+(1-sqrt(13))^n)/2.
|
|
4
| |
|
|
1, 1, 14, 40, 248, 976, 4928, 21568, 102272, 463360, 2153984, 9868288, 45584384, 209588224, 966189056, 4447436800, 20489142272, 94347526144, 434564759552, 2001299832832, 9217376780288, 42450351554560, 195509224472576
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,3
|
|
|
COMMENTS
| Binomial transform of A001022(powers of 13), with interpolated zeros . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Dec 20 2007
a(n-1) is the number of compositions of n when there are 1 type of 1 and 13 types of other natural numbers. [From Milan R. Janjic (agnus(AT)blic.net), Aug 13 2010]
|
|
|
FORMULA
| a(0)=1, a(1)=1, a(n)=2*a(n-1)+12*a(n-2) for n>=2 . G.f.:(1-x)/(1-2*x-12*x^2) - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Dec 12 2006
a(n)=Sum_{k, 0<=k<=n}A098158(n,k)*13^(n-k). - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Dec 20 2007
If p[1]=1, and p[i]=13, (i>1), and if A is Hessenberg matrix of order n defined by: A[i,j]=p[j-i+1], (i<=j), A[i,j]=-1,(i=j+1), and A[i,j]=0 otherwise. Then, for n>=1, a(n+1)=det A [From Milan R. Janjic (agnus(AT)blic.net), Apr 29 2010]
|
|
|
MATHEMATICA
| Expand[Table[((1 + Sqrt[13])^n + (1 - Sqrt[13])^n)/(2), {n, 0, 30}]] (*Artur Jasinski*)
|
|
|
CROSSREFS
| Cf. A091914.
Sequence in context: A069126 A124707 A126368 * A105869 A056034 A039404
Adjacent sequences: A125813 A125814 A125815 * A125817 A125818 A125819
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| Artur Jasinski (grafix(AT)csl.pl), Dec 10 2006
|
| |
|
|
