A063914 Odd numbers interlaced with numbers 3m+2.

1, 2, 3, 5, 5, 8, 7, 11, 9, 14, 11, 17, 13, 20, 15, 23, 17, 26, 19, 29, 21, 32, 23, 35, 25, 38, 27, 41, 29, 44, 31, 47, 33, 50, 35, 53, 37, 56, 39, 59, 41, 62, 43, 65, 45, 68, 47, 71, 49, 74, 51, 77, 53, 80, 55, 83, 57, 86, 59, 89, 61, 92, 63, 95, 65, 98, 67, 101, 69, 104, 71

Offset: 1

Author

Nancy Shaffer (nancys(AT)rose.net), Aug 30 2001

Keywords

• nonn
• easy

Comments

The reference gives the sequence without the initial 1 and then it is "alternate 3n+2 and 2n+3".

An alternative solution for this sequence is to consider the first second differences repeat giving 2, 3, 5, 5, 8, 7, 11, 12, 14, 14, 17, 16, 20, 21. - Lorraine Gregory, Ed.D. (lgregory(AT)lssu.edu), Jan 19 2009

References

• D. Dolan, J. Williamson and M. Muri, Mathematics Activities for Elementary School Teachers: A Problem Solving Approach, Addison Wesley Longman, Inc., NY, Fourth Edition (ISBN 0-201-61321-2), Chapter 1, Activity 2, #9.

Links

• Harry J. Smith, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (0,2,0,-1).

Programs

Maple

for n from 0 to 80 do printf(`%d,%d,`, 2*n+1, 3*n+2) od:

Mathematica

nn=50;Riffle[Range[1,2*nn,2],3*Range[0,nn]+2] (* Harvey P. Dale, Jan 16 2013 *)

PARI

a(n) = { if (n%2, n, 3*n/2 - 1) } \\ Harry J. Smith, Sep 02 2009

Formula

From Colin Barker, Mar 28 2012: (Start)

a(n) = 2*a(n-2)-a(n-4).

G.f.: x*(1+2*x+x^2+x^3)/((1-x)^2*(1+x)^2). (End)

a(n) = (5*n - 2 + (-1)^n*(n - 2))/4. - Andrew Howroyd, Dec 26 2024

Extensions

Better description from Brian Galebach, Sep 05 2001

More terms from James Sellers, Sep 25 2001