|
| |
|
|
A083068
|
|
7th row of number array A083064.
|
|
4
| |
|
|
1, 7, 55, 439, 3511, 28087, 224695, 1797559, 14380471, 115043767, 920350135, 7362801079, 58902408631, 471219269047, 3769754152375, 30158033218999, 241264265751991, 1930114126015927, 15440913008127415, 123527304065019319
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,2
|
|
|
COMMENTS
| Let A be the Hessenberg matrix of order n, defined by: A[1,j]=1, A[i,i]:=10, (i>1), A[i,i-1]=-1, and A[i,j]=0 otherwise. Then, for n>=1, a(n-1)=(-1)^(n-1)*charpoly(A,2). [From Milan R. Janjic (agnus(AT)blic.net), Feb 21 2010]
|
|
|
FORMULA
| a(n)=(6*8^n+1)/7 G.f. (1-2x)/((1-8x)(1-x)) E.g.f. (6*exp(8x)+exp(x))/7
a(n)=8*a(n-1)-1 (with a(0)=1) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Aug 08 2010]
|
|
|
EXAMPLE
| a(1)=8*1-1=7; a(2)=8*7-1=55; a(3)=8*55-1=439; a(4)=8*439-1=3511 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Aug 08 2010]
|
|
|
MATHEMATICA
| f[n_]:=8^n; lst={}; Do[a=f[n]; Do[a-=f[m], {m, n-1, 1, -1}]; AppendTo[lst, a/8], {n, 1, 30}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Feb 10 2010]
|
|
|
CROSSREFS
| Cf. A083067, A083066.
Sequence in context: A015564 A070997 A122372 * A097189 A049028 A096951
Adjacent sequences: A083065 A083066 A083067 * A083069 A083070 A083071
|
|
|
KEYWORD
| easy,nonn
|
|
|
AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Apr 21 2003
|
| |
|
|
