

A215695


a(n) = 5*a(n1)  6*a(n2) + a(n3) with a(0)=1, a(1)=0, a(2)=2.


10



1, 0, 2, 9, 33, 113, 376, 1235, 4032, 13126, 42673, 138641, 450293, 1462292, 4748343, 15418256, 50063514, 162556377, 527819057, 1713820537, 5564744720, 18068619435, 58668449392, 190495275070, 618534298433, 2008368291137, 6521130940157, 21173979252396, 68751478912175, 223234649986656, 724838355712626
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OFFSET

0,3


COMMENTS

The Berndttype sequence number 10 for the argument 2Pi/7 defined by the first trigonometric relation from section "Formula". For additional informations and particularly connections with another sequences of trigonometric nature  see comments to A215512 (a(n) is equal to the sequence c(n) in these comments) and WitulaSlota's reference (Section 3).
The following summation formula hold true (see comments to A215512): Sum{k=3,..,n} a(k) = 5*a(n1)  a(n2) + 1, n=3,4,...


LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000
Roman Witula and Damian Slota, New RamanujanType Formulas and QuasiFibonacci Numbers of Order 7, Journal of Integer Sequences, Vol. 10 (2007), Article 07.5.6
Index entries for linear recurrences with constant coefficients, signature (5,6,1).


FORMULA

sqrt(7)*a(n) = s(1)*c(1)^(2*n) + s(2)*c(2)^(2*n) + s(4)*c(4)^(2*n), where c(j):=2*cos(2*Pi*j/7) and s(j):=2*sin(2*Pi*j/7).
G.f.: (15*x+4*x^2)/(15*x+6*x^2x^3).
a(n) = A005021(n)  5*A005021(n1) + 4*A005021(n2).  R. J. Mathar, Aug 22 2012


EXAMPLE

We have a(8)=3*a(7)+3*a(5)6*a(2) and a(9)=3*a(8)+3*a(6)3*a(4)a(1).


MATHEMATICA

LinearRecurrence[{5, 6, 1}, {1, 0, 2}, 50]


PROG

(PARI) x='x+O('x^30); Vec((15*x+4*x^2)/(15*x+6*x^2x^3)) \\ G. C. Greubel, Apr 25 2018
(MAGMA) I:=[1, 0, 2]; [n le 3 select I[n] else 5*Self(n1)  6*Self(n2) + Self(n3): n in [1..30]]; // G. C. Greubel, Apr 25 2018


CROSSREFS

Cf. A215512 (the inverse binomial transform, up to signs), A215694.
Sequence in context: A122097 A073400 A048498 * A289600 A202206 A150921
Adjacent sequences: A215692 A215693 A215694 * A215696 A215697 A215698


KEYWORD

sign,easy


AUTHOR

Roman Witula, Aug 21 2012


STATUS

approved



