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A081188 6th binomial transform of (1,0,1,0,1,.....), A059841. 7
1, 6, 37, 234, 1513, 9966, 66637, 450834, 3077713, 21153366, 146120437, 1013077434, 7042713913, 49054856766, 342163294237, 2389039544034, 16692759230113, 116696726720166, 816114147588037, 5708984335850634 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Binomial transform of A081187.

a(n) is also the number of words of length n over an alphabet of seven letters, of which a chosen one appears an even number of times. See a comment in A007582, also for the crossrefs. for the 1- to 11- letter word cases. - Wolfdieter Lang, Jul 17 2017

LINKS

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

Takao Komatsu, Some recurrence relations of poly-Cauchy numbers, J. Nonlinear Sci. Appl., (2019) Vol. 12, Issue 12, 829-845.

Index entries for linear recurrences with constant coefficients, signature (12,-35).

FORMULA

a(n) = 12*a(n-1) -35*a(n-2), a(0)=1, a(1)=6.

G.f.: (1-6*x)/((1-5*x)*(1-7*x)).

E.g.f.: exp(6*x)*cosh(x).

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

MATHEMATICA

CoefficientList[Series[(1 - 6 x) / ((1 - 5 x) (1 - 7 x)), {x, 0, 20}], x] (* Vincenzo Librandi, Aug 07 2013 *)

LinearRecurrence[{12, -35}, {1, 6}, 30] (* Harvey P. Dale, Mar 24 2016 *)

PROG

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

(PARI) a(n)=5^n/2+7^n/2 \\ Charles R Greathouse IV, Oct 07 2015

CROSSREFS

Cf. A007582, A081186, A081189.

Sequence in context: A122898 A317629 A081912 * A218186 A154623 A196834

Adjacent sequences:  A081185 A081186 A081187 * A081189 A081190 A081191

KEYWORD

nonn,easy

AUTHOR

Paul Barry, Mar 11 2003

STATUS

approved

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Last modified June 15 00:00 EDT 2021. Contains 345041 sequences. (Running on oeis4.)