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A145139 Antidiagonal sums of A145153. 2
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified April 14 12:11 EDT 2021. Contains 342949 sequences. (Running on oeis4.)