Brian J. Tyrrell - cp's OEIS frontend

User: Brian J. Tyrrell

Brian J. Tyrrell has authored 2 sequences.

A218089 a(n) = n*((n+1)^n - n^(n-1)).

1, 14, 165, 2244, 35755, 659238, 13856521, 327596552, 8612579511, 249374246010, 7887780406957, 270660921021516, 10015416945711619, 397588957529910734, 16855928678721845265, 760132325936960344080, 36333256253671504279279

Offset: 1

Brian J. Tyrrell, Oct 20 2012

A178922 := proc(n)
    (n+1)^n-n^(n-1) ;
end proc:
A218089 := proc(n)
    n*A178922(n) ;
end proc: # R. J. Mathar, Oct 21 2012

a[n_] := n*((n + 1)^n - n^(n - 1))
Table[n*((n + 1)^n - n^(n - 1)), {n, 100}]

A218089[n]:=n*((n+1)^n-n^(n-1))$ makelist(A218089[n],n,1,30); /* Martin Ettl, Oct 29 2012 */

a(n) = n*A178922(n).

A217974 The ZEBRA Sequence.

Original entry on oeis.org

26, 5, 2, 18, 1, 24, 1, 0, 13, 6, 24, 6, 0, 12, 11, 24, 11, 0, 6, 12, 24, 12, 0, 5, 18, 24, 18, 0, 7, 19, 24, 19, 0, 11, 17, 24, 17, 0, 8, 13, 24, 13, 0, 9, 16, 24, 16, 0, 4, 15, 24, 15, 0, 12, 20, 24, 20, 0, 3, 12, 24, 12, 0, 17, 21, 24, 21, 0, 5, 7, 24, 7, 0, 16, 19, 24, 19, 0, 9, 8, 24, 8, 0, 10, 15, 24, 15, 0, 2, 14, 24, 14, 0, 13, 22, 24, 22, 0, 1, 11, 24, 11, 0, 21, 23, 24, 23, 0, 10, 3, 24, 3, 0, 13, 14, 24, 14, 0, 10, 11, 24, 11, 0, 4, 14, 24, 14, 0, 7, 20, 24, 20, 0, 7, 17, 24, 17, 0, 13, 17, 24, 17, 0, 4, 11, 24, 11, 0

Offset: 1

Brian J. Tyrrell, Oct 16 2012

nonn

If a=1, b=2...
Then ZEBRA = 26,5,2,18,1.
Let the 1st, 3rd, 5th, etc. terms of the sequence be "Black" numbers, and the 2nd, 4th, 6th, etc. be "White" numbers.
Using the first 5 terms as a starting point, to calculate the n-th term, one needs to calculate B(n), the n-th black number using B(n) = B(n-1) - B(n-2). If one runs out of Black numbers to calculate, switch over and calculate White numbers, using the formula W(n) = W(n-1) - W(n-2).
There are no negative terms, so if a negative term appears, multiply it by -1.
A pattern begins to appear: in every group of 5 after the first 8 terms, the 5th term = 0, the middle term = 24 and the 2nd term = 4th term.

			First 5 terms; 26,5,2,18,1
Black numbers = 26,  2,  1
White numbers = 5,  18
To calculate the 6th term, Use the formula B(n) = B(n-1) - B(n-2)
6th term = 2 - 26 = -24. But there are no negative terms, so 6th term = 24
7th term = 2 - 1  = 1
8th term = 1 - 1  = 0
We can no longer calculate Black numbers, so we switch to calculating White numbers.
9th term = 1st White term - 2nd White term = 5 - 18 = -13  => No negative terms
=> 9th term = 13
10th term = 18 - 24 = -6 => 6
11th term = 24 - 0 = 24

B(n) = |B(n-1) - B(n-2)|,

W(n) = |W(n-1) - W(n-2)|.

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User: Brian J. Tyrrell

A218089 a(n) = n*((n+1)^n - n^(n-1)).

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A217974 The ZEBRA Sequence.

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