Help extending equation -- sequence related to pentagonal numbers

Andrew Plewe aplewe at sbcglobal.net
Fri Dec 23 02:14:44 CET 2005


My new sequence follows from extending a group of partial equations for 
other sequences related to pentagonal/triangle numbers in the OEIS.  To 
demonstrate the pattern, I've listed the sequences in the OEIS with 
their corresponding partial generating equations.  I'd like to find a.) 
an equation that fully describes my new sequence, and b.) a general 
method for deriving equations for other similar sequences. "tri", here, 
represents the function for generating triangle numbers ((n * (n + 
1))/2:

A005449 = 0, 2, 7, 15, 26, 40, etc.  Equation to produce sequence from 
third term: 7 + 8(x) + (3 * tri(x-1))

A000326 = 0, 1, 5, 12, 22, 35, etc.  Equation to produce sequence from 
fourth term: 12 + 10(x) + (3 * tri(x-1))

A045943 = 0, 3, 9, 18, 30, 45, etc.  Equation to produce sequence from 
fourth term: 18 + 12(x) + (3 * tri(x-1))

A095794 = 1, 6, 14, 25, 39, 56, etc.  Equation to produce sequence from 
fourth term: 25 + 14(x) + (3 * tri(x-1))

And my new sequence:

A000001 = 3, 10, 20, 33, 49, 68, etc.  Equation to produce sequence 
from fourth term: 33 + 16(x) + (3 * tri(x-1))


As you can see there is a pattern to these generating equations.  
Looking at the equations already in the database for the sequences 
listed above, I was unable to determine a general method for generating 
equations which would fully describe sequences derived in this manner.  
I'm not sure if it's o.k. to submit equations that partially describe a 
sequence to the OEIS, so I'd like to find one which fully describes my 
sequence before submitting it.  Any help is appreciated.  Thanks!






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