A054145 Row sums of array T as in A054144.

0, 2, 12, 58, 256, 1072, 4336, 17112, 66304, 253280, 956608, 3579680, 13292544, 49039360, 179912448, 656874368, 2388205568, 8650598912, 31231020032, 112419973632, 403596148736, 1445463642112, 5165581660160, 18423238924288

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (8,-20,16,-4).

Formula

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

a(n) = ((n-2)*((2 + sqrt(2))^n + (2 - sqrt(2))^n) + sqrt(2)*((2 + sqrt(2))^n - (2 - sqrt(2))^n))/8. - G. C. Greubel, Jul 31 2019

Mathematica

LinearRecurrence[{8, -20, 16, -4}, {0, 2, 12, 58}, 30] (* G. C. Greubel, Jul 31 2019 *)

Prog

(PARI) my(x='x+O('x^30)); concat([0], Vec(2*x*(1-x)^2/(1-4*x+2*x^2)^2)) \\ G. C. Greubel, Jul 31 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 30); [0] cat Coefficients(R!( 2*x*(1-x)^2/(1-4*x+2*x^2)^2 )); // G. C. Greubel, Jul 31 2019
(Sage) (2*x*(1-x)^2/(1-4*x+2*x^2)^2).series(x, 30).coefficients(x, sparse=False) # G. C. Greubel, Jul 31 2019
(GAP) a:=[0, 2, 12, 58];; for n in [5..30] do a[n]:=8*a[n-1]-20*a[n-2] +16*a[n-3]-4*a[n-4]; od; a; # G. C. Greubel, Jul 31 2019

Crossrefs

Sequence in context: A268594 A100103 A281028 * A285364 A282435 A001758

Adjacent sequences: A054142 A054143 A054144 * A054146 A054147 A054148

Keyword

nonn

Author

Clark Kimberling, Mar 18 2000

Status

approved