A180678 The Ze2 sums of the Pell-Jacobsthal triangle A013609.

1, 2, 5, 16, 57, 206, 737, 2612, 9213, 32442, 114205, 402072, 1415713, 4985126, 17554489, 61816252, 217679141, 766531986, 2699251381, 9505089568, 33471028105, 117864194430, 415044573969, 1461529529924, 5146600421325

Offset

0,2

Comments

The a(n) represent the Ze2 sums of the Pell-Jacobsthal triangle A013609. See A180662 for information about these zebra and other chess sums.

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (6,-11,8).

Formula

a(n) = 6*a(n-1) - 11*a(n-2) + 8*a(n-3) with a(0)=1, a(1)=2 and a(2)= 5.

a(n) = Sum_{k=0..floor(n/2)} A013609(n+k,n-2*k).

G.f.: (1-4*x+4*x^2)/(1-6*x+11*x^2-8*x^3).

Maple

nmax:=24: a(0):=1: a(1):=2: a(2):=5: for n from 3 to nmax do a(n) := 6*a(n-1)-11*a(n-2)+8*a(n-3) od: seq(a(n), n=0..nmax);

Mathematica

LinearRecurrence[{6, -11, 8}, {1, 2, 5}, 30] (* or *) CoefficientList[ Series[(1-4*x+4*x^2)/(1-6*x+11*x^2-8*x^3), {x, 0, 30}], x] (* G. C. Greubel, Jun 06 2019 *)

Prog

(PARI) my(x='x+O('x^30)); Vec((1-4*x+4*x^2)/(1-6*x+11*x^2-8*x^3)) \\ G. C. Greubel, Jun 06 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1-4*x+4*x^2)/(1-6*x+11*x^2-8*x^3) )); // G. C. Greubel, Jun 06 2019
(Sage) ((1-4*x+4*x^2)/(1-6*x+11*x^2-8*x^3)).series(x, 30).coefficients(x, sparse=False) # G. C. Greubel, Jun 06 2019
(GAP) a:=[1, 2, 5];; for n in [4..30] do a[n]:=6*a[n-1]-11*a[n-2]+8*a[n-3]; od; a; # G. C. Greubel, Jun 06 2019

Crossrefs

Cf. A140413 (Ze1), A180678 (Ze2), A097117 (Ze3), A055588 (Ze4).

Sequence in context: A350906 A082789 A234278 * A072110 A323229 A197158

Adjacent sequences: A180675 A180676 A180677 * A180679 A180680 A180681

Keyword

easy,nonn

Author

Johannes W. Meijer, Sep 21 2010

Status

approved