a puxxle

[Lei Zhou]

A weird solution.  It might not make sense.

Step 1.
A056232:
3, 6, 11, 15, 18, 22, 25, 27, 30, 35, 39, 41, 44, 51, 59, 63, 66, 70, 73...

Step 2.
Seed 1, 3, 8:
define n(1)=1, n(2)=3, n3=(8).

Step 3.
define m(i)=n(i)+n(i+2)
==> m(1)=1+8=9

Step 4.
define m(i+1)=m(i)*2+A056232(i)
==> series m:
9, 21, 48, 107, 229, 476, 974, 1973, 3973, 7976, 15987, 32013, 64067, 
128178, 256407, 512873, 1025809, 2051684, 4103438, 8206949...

Step 5.
According to definition in step 3:
m(2)=n(2)+n(4) ==> n(4)=21-3=18;
m(3)=n(3)+n(5) ==> n(5)=48-8=40;
m(4)=n(4)+n(6) ==> n(6)=107-18=89;
m(5)=n(5)+n(7) ==> n(7)=229-40=189;
m(6)=n(6)+n(8) ==> n(8)=476-89=387;
m(7)=n(7)+n(9) ==> n(9)=974-189=785;
...

Step 6.
So, the missing term of A117713 is 40, and the first 20 terms are:
1,3,8,18,40,89,189,387,785,1586,3188,6390,12799,25623,51268,102555,205139,410318,820670,1641366...

Step 7.
 From definition of step 3, and 4 ==>
n(k+3)=2*n(k)-n(k+1)+2*n(k+2)+A056232(k)

deal.

Cheers,

Lei


At 23:00 04/13/2006, you wrote:
>Dear Seqfans:
>Someone just sent this in.  I gave it an A-number.  But I can't
>add it to the OEIS until the missing term is filled in. Any ideas?
>The differences are suggestive
>
>%I A117713
>%S A117713 1,3,8,18,__,89,189
>%N A117713 This sequence was a question on a civil service test a 
>friend of mine took. They had to fill in the blank number. Is there 
>an answer to this??.
>%O A117713 0,2
>%K A117713 nonn
>%A A117713 Louis Ciotti (lciotti(AT)twcny.rr.com), Apr 13 2006
>
>Differences: 2 5 10 a b 100 , but a+b = 71, which is ugly.
>
>Neil