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

1,2

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

Formula

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). - Colin Barker, Mar 28 2012

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 *)

Prog

(PARI) { for (n=1, 1000, if (n%2, a=n, a=3*n/2 - 1); write("b063914.txt", n, " ", a) ) } [Harry J. Smith, Sep 02 2009]

Crossrefs

Sequence in context: A095413 A134871 A267453 * A209187 A357259 A166250

Adjacent sequences: A063911 A063912 A063913 * A063915 A063916 A063917

Keyword

nonn,easy

Author

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

Extensions

Better description from Brian Galebach, Sep 05, 2001

More terms from James A. Sellers, Sep 25 2001

Status

approved