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A081201
7th binomial transform of (0,1,0,1,0,1,....), A000035.
8
0, 1, 14, 148, 1400, 12496, 107744, 908608, 7548800, 62070016, 506637824, 4113568768, 33271347200, 268347559936, 2159841173504, 17357093552128, 139326933401600, 1117436577120256, 8956419276406784, 71752914167922688, 574632673083392000, 4600717543107198976
OFFSET
0,3
COMMENTS
Binomial transform of A081200.
Conjecture (verified up to a(8)): Number of collinear 6-tuples of points in a 6 X 6 X 6 X... n-dimensional cubic grid. [R. H. Hardin, May 23 2010]
From Wolfdieter Lang, Jul 17 2017: (Start)
For a combinatorial interpretation of a(n) with special 8-letter words of length n see the comment in A081200 on the 7-letter analog.
The binomial transform of {a(n)}_{n >= 0} is A081202, the 9-letter analog.
(End)
FORMULA
a(n) = 14*a(n-1) - 48*a(n-2) with n>1, a(0)=0, a(1)=1.
G.f.: x/((1-6*x)*(1-8*x)).
a(n) = 8^n/2 - 6^n/2.
MATHEMATICA
CoefficientList[Series[x/((1 - 6 x) (1 - 8 x)), {x, 0, 20}], x] (* Vincenzo Librandi, Aug 07 2013 *)
LinearRecurrence[{14, -48}, {0, 1}, 30] (* Harvey P. Dale, Oct 24 2022 *)
PROG
(Magma) [8^n/2-6^n/2: n in [0..25]]; // Vincenzo Librandi, Aug 07 2013
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Paul Barry, Mar 11 2003
EXTENSIONS
Name clarified by Pontus von Brömssen, Nov 11 2020
STATUS
approved