|
Search: id:A118061
|
|
|
| A118061 |
|
a(n)=9800n^2-5740n-4059; a(n)+(a(n)+1)+...+(a(n)+9800n+6929)=(a(n)+9800n+6930)+...+(a(n)+19600n+4059); a(n)+19600n+4059=a(n+1)-1; a(n+1)-1=a(n)+19600n+4059. |
|
+0
5
|
|
| 1, 23661, 66921, 129781, 212241, 314301, 435961, 577221, 738081, 918541, 1118601, 1338261, 1577521, 1836381, 2114841, 2412901, 2730561, 3067821, 3424681, 3801141, 4197201, 4612861, 5048121, 5502981, 5977441, 6471501
(list; graph; listen)
|
|
|
OFFSET
|
1,2
|
|
|
COMMENT
|
In general, all sequences of equations which contain every positive integer in order exactly once (a pair wise equal summed, ordered partition of the positive integers) may be defined as follows: For all k, let x(k)=A001652(k) and z(k)=A001653(k). Then if we define a(n) to be (x(k)+z(k))n^2-(z(k)-1)n-x(k), the following equation is true: a(n)+(a(n)+1)+...+(a(n)+(x(k)+z(k))n+(2x(k)+z(k)-1)/2)=(a(n)+ (x(k)+z(k))n+(2x(k)+z(k)+1)/2)+...+(a(n)+2(x(k)+z(k))n+x(k)); a(n)+2(x(k)+z(k))n+x(k))=a(n+1)-1; e.g., in this sequence, x(5)=A001652(5)=4059 and z(5)=A001653(5)=5741; cf. A000290,A118057-A118060.
|
|
FORMULA
|
a(n)+(a(n)+1)+...+(a(n)+576n+203)=35(140n-41)(140n+29)(140n+99); e.g., 66921+66922+...+103250=3091156215=35*379*449*519.
|
|
EXAMPLE
|
a(3)= 9800*3^2-5740*3-4059=66921, a(4)=9800*4^2-5740*4-4059=129781 and 66921+66922+...+103250=103251+...+129780
|
|
CROSSREFS
|
Sequence in context: A133968 A031847 A069334 this_sequence A011254 A066234 A084691
Adjacent sequences: A118058 A118059 A118060 this_sequence A118062 A118063 A118064
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Charlie Marion (charliemath(AT)optonline.net), Apr 26 2006
|
|
EXTENSIONS
|
Corrected by T. D. Noe (noe(AT)sspectra.com), Nov 13 2006
|
|
|
Search completed in 0.002 seconds
|
