A067066 Number of Gnutella users reachable with given connections and hops.

1, 2, 1, 3, 4, 1, 4, 9, 6, 1, 5, 16, 21, 8, 1, 6, 25, 52, 45, 10, 1, 7, 36, 105, 160, 93, 12, 1, 8, 49, 186, 425, 484, 189, 14, 1, 9, 64, 301, 936, 1705, 1456, 381, 16, 1, 10, 81, 456, 1813, 4686, 6825, 4372, 765, 18, 1, 11, 100, 657, 3200, 10885, 23436, 27305, 13120, 1533, 20, 1

Offset

1,2

Links

Table of n, a(n) for n=1..66.

Jordan Ritter, Why Gnutella Can't Scale. No, Really.

Formula

T(n,k) = n * Sum_{i=0..k-1} (n-1)^i.

Example

     1      1      1      1      1      1      1 ...
     2      4      6      8     10     12     14 ...
     3      9     21     45     93    189    381 ...
     4     16     52    160    484   1456   4372 ...
     5     25    105    425   1705   6825  27305 ...
     6     36    186    936   4686  23436 117186 ...
     7     49    301   1813  10885  65317 391909 ...

Crossrefs

Cf. A104881.

Sequence in context: A093375 A103283 A104698 * A210219 A125103 A171275

Adjacent sequences: A067063 A067064 A067065 * A067067 A067068 A067069

Keyword

nonn,tabl,easy

Author

Michael Somos, Feb 17 2002

Extensions

Offset corrected, R. J. Mathar, May 22 2016

Status

approved