A137864 a(n) = n^4 - 10n^3 + 35n^2 - 48n + 23.

1, 3, 5, 7, 33, 131, 373, 855, 1697, 3043, 5061, 7943, 11905, 17187, 24053, 32791, 43713, 57155, 73477, 93063, 116321, 143683, 175605, 212567, 255073, 303651, 358853, 421255, 491457, 570083, 657781, 755223, 863105, 982147, 1113093, 1256711, 1413793

Offset

1,2

Comments

This sequence appears at first to be the sequence of odd numbers but then rapidly becomes something different altogether. It is a good example of why more than a few terms are needed to check a hypothesis.

Useful for practicing the method of finite differences.

References

A. Watson and J. Mason, Mathematics as a Constructive Activity, LEA London, 2005, p. 162.

Links

Nathaniel Johnston, Table of n, a(n) for n = 1..5000

Mike Shepperd, Method of Finite Differences

Index entries for linear recurrences with constant coefficients, signature (5, -10, 10, -5, 1).

Formula

O.g.f.: -x*(1-2*x+2*x^3+23*x^4)/(-1+x)^5 . - R. J. Mathar, Feb 19 2008

a(0)=1, a(1)=3, a(2)=5, a(3)=7, a(4)=33, a(n)=5*a(n-1)-10*a(n-2)+ 10*a(n-3)- 5*a(n-4)+a(n-5). - Harvey P. Dale, Aug 18 2011

Example

a(5) = 33 is the first term that breaks with the odd number pattern.

Maple

A137864 := proc(n) return n^4-10*n^3+35*n^2-48*n+23: end: seq(A137864(n), n=1..100); # Nathaniel Johnston, May 09 2011

Mathematica

Table[n^4-10n^3+35n^2-48n+23, {n, 50}] (* or *) LinearRecurrence[ {5, -10, 10, -5, 1}, {1, 3, 5, 7, 33}, 50] (* Harvey P. Dale, Aug 18 2011 *)

Crossrefs

Cf. A005408.

Sequence in context: A029508 A256935 A095714 * A256154 A069969 A067232

Adjacent sequences: A137861 A137862 A137863 * A137865 A137866 A137867

Keyword

easy,nonn

Author

Christopher Martin (christopher.j.martin(AT)gmail.com), Feb 17 2008

Extensions

More terms from R. J. Mathar, Feb 19 2008

Status

approved