A081201 7th binomial transform of (0,1,0,1,0,1,....), A000035.

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)

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Index entries for linear recurrences with constant coefficients, signature (14,-48).

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) = (1/2)*(8^n - 6^n).

E.g.f.: exp(7*x)*sinh(x). - G. C. Greubel, Nov 10 2024

Mathematica

CoefficientList[Series[x/((1 - 6 x) (1 - 8 x)), {x, 0, 30}], x] (* Vincenzo Librandi, Aug 07 2013 *)
LinearRecurrence[{14, -48}, {0, 1}, 30] (* Harvey P. Dale, Oct 24 2022 *)

Prog

(Magma) [(8^n-6^n)/2: n in [0..30]]; // Vincenzo Librandi, Aug 07 2013
(SageMath)
A081201=BinaryRecurrenceSequence(14, -48, 0, 1)
[A081201(n) for n in range(41)] # G. C. Greubel, Nov 10 2024

Crossrefs

Cf. A000035, A016169, A016170, A081200, A081202.

Sequence in context: A302994 A207259 A016170 * A065899 A162965 A067103

Adjacent sequences: A081198 A081199 A081200 * A081202 A081203 A081204

Keyword

nonn,easy

Author

Paul Barry, Mar 11 2003

Extensions

Name clarified by Pontus von Brömssen, Nov 11 2020

Status

approved