Examples of Sequence Numbers: Combinatorial Functions
C (n,2): The number of ways to choose two
items from a group of n items. (This
sequence is also called the Triangular numbers, and the third diagonal in
Pascal’s Triangle. At the end of this
post I will show how this sequence is related the 3, 3, 1 Tribonacci
sequence.)
The Sequence Number is: 999,997,000,002,999,999
1/999997000002999999 =
0.
000000 000000 000001 000003 000006 000010 000015 000021 000028 000036 000045 000055 000066 000078 …
Terms are written in six digit strings.
Compare with OEIS sequence A000217.

C (n, 3): The number of ways to choose
three items from a group of n items.
(This sequence is also called the Tetrahedral numbers and the fourth
diagonal in Pascal’s Triangle.)
The Sequence Number is: 999,996,000,005,999,996,000,
001
1/999996000005999996000
001 =
0.
000000 000000 000000 000001 000004 000010 000020 000035 000056 000084 000120 000165 000220 000286 …
Terms are written in six digit strings.
Compare with OEIS sequence A000292.

C (n, 4): The number of ways to choose
four items from a group of n items.
The Sequence Number is: 999,995,000,009,999,990,000,
004,999,999
1/9999950000099999900000
04999999 =
0.
000000 000000 000000 000000 000001 000005 000015 000035 000070 000126 000210 000330 000495 000715 001001 001365 001820 …
Terms are written in six digit strings.
These terms are also the numbers found in
the fifth diagonal of Pascal’s Triangle.
Compare with OEIS sequence A000332.

C (n, 5): The number of ways to choose
five items from a group of n items.
The Sequence Number is: 999,994,000,014,999,980,000,
014,999,994,000,001
1/9999940000149999800000
14999994000001 =
0.
000000 000000 000000 000000 000000 000001 000006 000021 000056 000126 000252 000462 000792 001287 002002 003003 004368 …
Terms are written in six digit strings.
These terms are also the numbers found in
the sixth diagonal of Pascal’s Triangle.
Compare with OEIS sequence A000389.

See more examples at: SequenceNumbers.Blogspot.Com
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