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A192395 Main (or principal) sequence for a(n) = 2*a(n-1) - 2*a(n-2) + a(n-3) + 2*a(n-4). 2
0, 0, 0, 1, 2, 2, 1, 2, 8, 17, 22, 22, 33, 78, 156, 233, 298, 442, 833, 1546, 2464, 3553, 5390, 9230, 16161, 26358, 40404, 62713, 103298, 174290, 285505, 451154, 712184, 1156145, 1910086, 3122374, 5005089, 7987806, 12907980 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Autosequence of first kind. The basic sequence is c(n)=(-1)^(n+1) * A001045(n).

a(n) and differences:

   0,  0,  0,  1,  2,  2,   1,

   0,  0,  1,  1,  0, -1,   1,

   0,  1,  0, -1, -1,  2,   5,

   1, -1, -1,  0,  3,  3,  -2,

  -2,  0,  1,  3,  0, -5,  -5,

   2,  1,  2, -3, -5,  0, -11,

  -1,  1, -5, -2,  5, 11,   0.

Diagonal: A001045, A001045 and (0,A077925), A078008 and A151575, A014551, A140966, A083581.

The corresponding sequence of second kind (companion in the sense of autosequences) is

b(n)=0,0,2,3,2,0,3,14,26,27,22,44,... The recurrence is the same.

b(n) and differences are

   0,  0,  2,  3,   2,  0,

   0,  2,  1, -1,  -2,  3,

   2, -1, -2, -1,   5,  8,

  -3, -1,  1,  6,   3, -7,

   2,  2,  5, -3, -10, -5,

   0,  3, -8, -7,   5, 22.

Main diagonal = 2*first upper diagonal = 2*c(n) = (-1)^(n+1) * A078008(n+1).

Inverse binomial sequence of both sequences are the sequence signed.

LINKS

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

OEIS Wiki, Autosequence

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

FORMULA

G.f.: ( -x^3 ) / ( (2*x^2 - x + 1)*(x^2 + x - 1) ). - R. J. Mathar, Jul 14 2011

a(n) = -A107920(n)/3 + A000045(n)/3. - R. J. Mathar, Jul 14 2011

MATHEMATICA

LinearRecurrence[{2, -2, 1, 2}, {0, 0, 0, 1}, 100] (* Vincenzo Librandi, Nov 25 2011 *)

PROG

(MAGMA) I:=[0, 0, 0, 1]; [n le 4 select I[n] else 2*Self(n-1)-2*Self(n-2)+Self(n-3)+2*Self(n-4): n in [1..50]]; // Vincenzo Librandi, Nov 25 2011

CROSSREFS

Sequence in context: A162663 A005007 A188792 * A014243 A124839 A294076

Adjacent sequences:  A192392 A192393 A192394 * A192396 A192397 A192398

KEYWORD

nonn,easy

AUTHOR

Paul Curtz, Jun 29 2011

STATUS

approved

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Last modified May 24 16:47 EDT 2019. Contains 323533 sequences. (Running on oeis4.)