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 A083066 5th row of number array A083064. 13
 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 Mudit Aggarwal and Samrith Ram, Generating Functions for Straight Polyomino Tilings of Narrow Rectangles, J. Int. Seq., Vol. 26 (2023), Article 23.1.4. R. J. Mathar, Tilings of rectangular regions by rectangular tiles: Counts derived from transfer matrices, arXiv:1406.7788 [math.CO], 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_{i=0..n-1} 6^i 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. A083064, 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 December 11 13:16 EST 2023. Contains 367727 sequences. (Running on oeis4.)