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A081200 6th binomial transform of (0,1,0,1,0,1,....), A000035. 7
0, 1, 12, 109, 888, 6841, 51012, 372709, 2687088, 19200241, 136354812, 964249309, 6798573288, 47834153641, 336059778612, 2358521965909, 16540171339488, 115933787267041, 812299450322412, 5689910849522509, 39848449432985688 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Binomial transform of A081199.

Conjecture (verified up to a(9)): Number of collinear 5-tuples of points in a 5 X 5 X 5 X... n-dimensional cubic grid [R. H. Hardin, May 23 2010] [Ron 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 (12,-35).

FORMULA

a(n) = 12*a(n-1) -35*a(n-2), a(0)=0, a(1)=1.

G.f.: x/((1-5*x)*(1-7*x)).

a(n) = 7^n/2 - 5^n/2.

a(n) = sum( k=0..n-1, 7^k * 5^(n-k-1) ), with a(0)=0. [Reinhard Zumkeller, Aug 01 2010]

a(n) = A121213(n)/2. [Reinhard Zumkeller, Aug 01 2010]

MATHEMATICA

CoefficientList[Series[x / ((1 - 5 x) (1 - 7 x)), {x, 0, 20}], x] (* Vincenzo Librandi, Aug 07 2013 *)

LinearRecurrence[{12, -35}, {0, 1}, 30] (* Harvey P. Dale, Feb 07 2014 *)

PROG

(Sage) [lucas_number1(n, 12, 35) for n in xrange(0, 21)]# Zerinvary Lajos, Apr 27 2009

(MAGMA) [7^n/2-5^n/2: n in [0..25]]; // Vincenzo Librandi, Aug 07 2013

CROSSREFS

Cf. A016161.

Sequence in context: A128877 A085797 A016161 * A016214 A037581 A177071

Adjacent sequences:  A081197 A081198 A081199 * A081201 A081202 A081203

KEYWORD

nonn,easy

AUTHOR

Paul Barry, Mar 11 2003

STATUS

approved

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Last modified May 26 12:59 EDT 2017. Contains 287095 sequences.