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A081199 5th binomial transform of (0,1,0,1,.....), A000035. 7
0, 1, 10, 76, 520, 3376, 21280, 131776, 807040, 4907776, 29708800, 179301376, 1080002560, 6496792576, 39047864320, 234555621376, 1408407470080, 8454739787776, 50745618595840, 304542431051776, 1827529464217600 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Binomial transform of A005059.

Conjecture (verified up to a(9)): Number of collinear 4-tuples of points in a 4 X 4 X 4 X... n-dimensional cubic grid [From R. H. Hardin, May 24 2010]

LINKS

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

Index entries for linear recurrences with constant coefficients, signature (10,-24).

FORMULA

a(n) = 10*a(n-1)-24*a(n-2) with n>1, a(0)=0, a(1)=1.

G.f.: x/((1-4*x)*(1-6*x)).

a(n) = 6^n/2 - 4^n/2.

MAPLE

seq(add(2^(2*n-k)*binomial(n, k)/2, k=1..n), n=0..20); # [From Zerinvary Lajos, Apr 18 2009]

MATHEMATICA

CoefficientList[Series[x / ((1 - 4 x) (1 - 6 x)), {x, 0, 30}], x] (* Vincenzo Librandi, Aug 07 2013 *)

PROG

(MAGMA) [6^n/2-4^n/2: n in [0..25]]; // Vincenzo Librandi, Aug 07 2013

CROSSREFS

Cf. A016149.

Sequence in context: A061319 A223994 A016149 * A198692 A215465 A169584

Adjacent sequences:  A081196 A081197 A081198 * A081200 A081201 A081202

KEYWORD

nonn,easy

AUTHOR

Paul Barry, Mar 11 2003

STATUS

approved

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Last modified March 26 18:46 EDT 2017. Contains 284137 sequences.