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A083066 5th row of number array A083064. 12
1, 5, 29, 173, 1037, 6221, 37325, 223949, 1343693, 8062157, 48372941, 290237645, 1741425869, 10448555213, 62691331277, 376147987661, 2256887925965, 13541327555789, 81247965334733, 487487792008397, 2924926752050381 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Let A be the Hessenberg matrix of order n, defined by: A[1,j]=1, A[i,i]:=8, (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). [Milan Janjic, Feb 21 2010]

An Engel expansion of 3/2 to the base b := 6/5 as defined in A181565, with the associated series expansion 3/2 = b + b^2/5 + b^3/(5*29) + b^4/(5*29*173) + .... Cf. A007051. - Peter Bala, Oct 29 2013

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

R. J. Mathar, Tilings of rectangular regions by rectangular tiles: Counts derived from transfer matrices, arXiv:1406.7788 (2014), eq (43).

Index entries for linear recurrences with constant coefficients, signature (7,-6).

FORMULA

a(n) = (4*6^n+1)/5.

G.f.: (1-2*x)/((1-6*x)*(1-x)).

E.g.f.: (4*exp(6*x)+exp(x))/5.

a(n) = 6*a(n-1)-1 with n>0, a(0)=1. - Vincenzo Librandi, Aug 08 2010

a(n) = 7*a(n-1)-6*a(n-2). - Vincenzo Librandi, Nov 04 2011

a(n) = 6^n - sum(6^i, i=0..n-1) for n>0. [Bruno Berselli, Jun 20 2013]

MATHEMATICA

f[n_]:=6^n; lst={}; Do[a=f[n]; Do[a-=f[m], {m, n-1, 1, -1}]; AppendTo[lst, a/6], {n, 1, 30}]; lst (* Vladimir Joseph Stephan Orlovsky, Feb 10 2010 *)

PROG

(MAGMA) [(4*6^n+1)/5: n in [0..30]]; // Vincenzo Librandi, Nov 06 2011

CROSSREFS

Cf. A083065, A083067. A007051, A007583.

Sequence in context: A122370 A088349 A272802 * A327557 A163611 A160906

Adjacent sequences:  A083063 A083064 A083065 * A083067 A083068 A083069

KEYWORD

nonn,easy

AUTHOR

Paul Barry, Apr 21 2003

STATUS

approved

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Last modified January 20 12:43 EST 2022. Contains 350472 sequences. (Running on oeis4.)