## Tuesday, October 6, 2015

### Some More Examples of Sequence Numbers

10/06/2015

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

David