cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A158926 First differences of A158916.

Original entry on oeis.org

0, 0, 0, -9, 27, -54, 99, -189, 378, -765, 1539, -3078, 6147, -12285, 24570, -49149, 98307, -196614, 393219, -786429, 1572858, -3145725, 6291459, -12582918, 25165827, -50331645, 100663290, -201326589, 402653187, -805306374, 1610612739, -3221225469, 6442450938
Offset: 0

Views

Author

Paul Curtz, Mar 31 2009

Keywords

Links

Formula

a(n) = -3a(n-1)-3a(n-2)-2a(n-3), n > 3.
a(n) = 9*(-1)^n*A024495(n+1) .
G.f.: -9*x^3/((2*x+1)*(1+x+x^2)). - R. J. Mathar, Apr 08 2009

Extensions

Edited and extended by R. J. Mathar, Apr 08 2009

A158927 a(n) = -3a(n-1) - 3a(n-2) - 2a(n-3), n > 3.

Original entry on oeis.org

2, 2, 2, -7, 11, -16, 29, -61, 128, -259, 515, -1024, 2045, -4093, 8192, -16387, 32771, -65536, 131069, -262141, 524288, -1048579, 2097155, -4194304, 8388605, -16777213, 33554432, -67108867, 134217731, -268435456, 536870909, -1073741821, 2147483648
Offset: 0

Views

Author

Paul Curtz, Mar 31 2009

Keywords

Comments

The inverse binomial transform of A153130, after dropping A153130(0).
The inverse binomial transform of the full A153130 is A158916.
Dropping two initial terms of A153130 yields A158935, dropping three yields essentially a sign-reversed version of A158916, dropping 4 essentially the sequence here.

Links

Crossrefs

Same recurrence as A131562, A158916, A158926.

Programs

  • GAP
    a := [2,2,2,-7];; for n in [5..10^3] do a[n] := -3*a[n-1] - 3*a[n-2] - 2*a[n-3]; od; a; # Muniru A Asiru, Jan 27 2018
  • Maple
    a := proc(n) option remember: if n=0 then 2 elif n=1 then 2 elif n=2 then 2 elif n=3 then -7 elif n>=4 then -3*procname(n-1) - 3*procname(n-2) - 2*procname(n-3) fi; end:
seq(a(n), n=0..100); # Muniru A Asiru, Jan 27 2018

Formula

a(n) = -3a(n-1) - 3a(n-2) - 2a(n-3), with a(0)=a(1)=a(2)=2, a(3)=-7.
a(n) = (-1)^(n+1)*A157823(n) - A099838(n+3).
G.f.: (2+8*x+14*x^2+9*x^3)/((2*x+1)*(1+x+x^2)). - R. J. Mathar, Apr 09 2009
a(0)=2; a(n) = (1/2)*(-2)^n - 3*cos(2*Pi*n/3) + sqrt(3)*sin(2*Pi*n/3) for n >= 1. - Richard Choulet, Apr 23 2009

Extensions

Edited and extended by R. J. Mathar, Apr 09 2009

A158935 a(n)= -3a(n-1)-3a(n-2)-2a(n-3), n>3. a(0)=4, a(1)=4, a(2)=-5, a(3)=4.

Original entry on oeis.org

4, 4, -5, 4, -5, 13, -32, 67, -131, 256, -509, 1021, -2048, 4099, -8195, 16384, -32765, 65533, -131072, 262147, -524291, 1048576, -2097149, 4194301, -8388608, 16777219, -33554435, 67108864, -134217725, 268435453, -536870912, 1073741827, -2147483651
Offset: 0

Views

Author

Paul Curtz, Mar 31 2009

Keywords

Comments

The third column of the array of differences described in A153130. The first two columns are in A158916 and A158987. Taking differences like in A158926 keeps the recurrence.
Also the inverse binomial transform of A153130 if the first two items of A153130 are omitted.

Links

Programs

  • Mathematica
    Join[{4},LinearRecurrence[{-3,-3,-2},{4,-5,4},50]] (* Harvey P. Dale, May 25 2011 *)

Formula

a(n)= A154589(n) + A099838(n+2).
G.f.: (4+16*x+19*x^2+9*x^3)/((2*x+1)*(1+x+x^2)). - R. J. Mathar, Apr 08 2009

Extensions

Partially edited and extended by R. J. Mathar, Apr 08 2009
Edited by N. J. A. Sloane, Apr 08 2009
Showing 1-3 of 3 results.

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