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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