A145139 Antidiagonal sums of A145153.

0, 1, 1, 2, 4, 9, 18, 36, 72, 145, 291, 583, 1167, 2336, 4675, 9354, 18713, 37433, 74876, 149766, 299551, 599128, 1198292, 2396634, 4793337, 9586769, 19173669, 38347519, 76695288, 153390921, 306782318, 613565293, 1227131493, 2454264238

Offset

0,4

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (3,-2,0,1,-2).

Formula

G.f.: x*(1-x)^2 / ((1-2*x)*(1-x-x^4)).

Maple

a:= n-> (Matrix([[4, 2, 1, 1, 0]]). Matrix (5, (i, j)-> if i=j-1 then 1 elif j=1 then [3, -2, 0, 1, -2][i] else 0 fi)^n)[1, 5]: seq(a(n), n=0..40);

Mathematica

CoefficientList[Series[x*(1-x)^2/((1-2*x)*(1-x-x^4)), {x, 0, 40}], x] (* Vincenzo Librandi, Jun 06 2013 *)

Prog

(PARI) my(x='x+O('x^40)); concat([0], Vec(x*(1-x)^2/((1-2*x)*(1-x-x^4)))) \\ G. C. Greubel, May 21 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 40); [0] cat Coefficients(R!( x*(1-x)^2/((1-2*x)*(1-x-x^4)) )); // G. C. Greubel, May 21 2019
(Sage) (x*(1-x)^2/((1-2*x)*(1-x-x^4))).series(x, 40).coefficients(x, sparse=False) # G. C. Greubel, May 21 2019
(GAP) a:=[0, 1, 1, 2, 4];; for n in [6..40] do a[n]:=3*a[n-1]-2*a[n-2]+a[n-4] -2*a[n-5]; od; a; # G. C. Greubel, May 21 2019

Crossrefs

Cf. A145153, A000004, A000012, A001477, A000217, A000292, A145126, A145127, A145128, A145129, A145130, A017898, A003269, A098578, A145131, A145132, A145133, A145134, A145135, A145136, A145137.

Sequence in context: A111662 A253585 A119027 * A033138 A155803 A293352

Adjacent sequences: A145136 A145137 A145138 * A145140 A145141 A145142

Keyword

nonn,easy

Author

Alois P. Heinz, Oct 03 2008

Status

approved