A061891 -id:A061891 - cp's OEIS frontend

A168074 Duplicate of A061891.

1, 1, 4, 7, 7, 10, 13, 13, 16, 19, 19, 22, 25, 25, 28, 31, 31, 34, 37, 37, 40, 43, 43, 46, 49, 49, 52, 55, 55, 58, 61, 61, 64, 67, 67, 70, 73, 73, 76, 79, 79, 82, 85, 85, 88, 91, 91, 94, 97, 97, 100, 103, 103, 106, 109, 109, 112, 115, 115, 118

Offset: 0

Paul Barry, Nov 18 2009

dead

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

I:=[1,1,4,7]; [n le 4 select I[n] else Self(n-1)+Self(n-3)-Self(n-4): n in [1..70]]; // Vincenzo Librandi, Jul 10 2016

LinearRecurrence[{1, 0, 1, -1}, {1, 1, 4, 7}, 50] (* G. C. Greubel, Jul 09 2016 *)
CoefficientList[Series[(1 + 3 x^2 + 2 x^3) / ((1 - x)^2 (1 + x + x^2)), {x, 0, 60}], x] (* Vincenzo Librandi, Jul 10 2016 *)

Vec((1+3*x^2+2*x^3)/((1-x)^2*(1+x+x^2)) + O(x^70)) \\ Michel Marcus, Dec 03 2014

G.f.: (1+3x^2+2x^3)/((1-x)^2*(1+x+x^2)).
a(n) = A168075(n)/(-3)^n.
a(n) = A061891(n). - Georg Fischer, Oct 14 2018

Corrected by R. J. Mathar, Dec 03 2014

A168075 Expansion of (1+27x^2-54x^3)/((1+3x)^2*(1-3x+9 x^2)).

Original entry on oeis.org

1, -3, 36, -189, 567, -2430, 9477, -28431, 104976, -373977, 1121931, -3897234, 13286025, -39858075, 133923132, -444816117, 1334448351, -4390765542, 14334558093, -43003674279, 139471376040, -449795187729, 1349385563187, -4330586226042, 13839047287569

Offset: 0

Paul Barry, Nov 18 2009

Hankel transform of A168076.

G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (-3,0,-27,-81).

Cf. A061891, A168076.

I:=[1,-3,36,-189]; [n le 4 select I[n] else -3*Self(n-1)-27*Self(n-3)-81*Self(n-4): n in [1..30]]; // Vincenzo Librandi, Jul 10 2016

LinearRecurrence[{-3, 0, -27, -81}, {1, -3, 36, -189}, 50] (* G. C. Greubel, Jul 09 2016 *)
CoefficientList[Series[(1 + 27 x^2 - 54 x^3) / ((1 + 3 x)^2 (1 - 3 x + 9 x^2)), {x, 0, 40}], x] (* Vincenzo Librandi, Jul 10 2016 *)

Vec((1+27*x^2-54*x^3)/((1+3*x)^2*(1-3*x+9*x^2))+ O(x^30)) \\ Michel Marcus, Dec 03 2014

a(n) = (-3)^n*A061891(n).

a(n) = 2*(-3)^n*n + 3^n*(sin(Pi*n/3)/sqrt(3) + cos(Pi*n/3)). - Ilya Gutkovskiy, Jul 10 2016

Corrected by R. J. Mathar, Dec 03 2014

cp's OEIS Frontend

A168074 Duplicate of A061891.

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