|
Search: id:A057145
|
|
|
| A057145 |
|
Square array T(n,k) of polygonal numbers T(n,k) = ((n-2)*k^2-(n-4)*k)/2, n >= 2, k >= 1, read by antidiagonals. |
|
+0
26
|
|
| 1, 1, 2, 1, 3, 3, 1, 4, 6, 4, 1, 5, 9, 10, 5, 1, 6, 12, 16, 15, 6, 1, 7, 15, 22, 25, 21, 7, 1, 8, 18, 28, 35, 36, 28, 8, 1, 9, 21, 34, 45, 51, 49, 36, 9, 1, 10, 24, 49, 55, 66, 70, 64, 45, 10, 1, 11, 27, 46, 65, 81, 91, 92, 81, 55, 11
(list; table; graph; listen)
|
|
|
OFFSET
|
2,3
|
|
|
COMMENT
|
Stuart M. Ellerstein (ELLERSTEIN(AT)aol.com) remarks that T(2n+4,n) = n^3, Aug 28, 2000
|
|
REFERENCES
|
A. H. Beiler, Recreations in the Theory of Numbers. New York: Dover, p. 189, 1966.
|
|
FORMULA
|
T(n, k) =T(n-1, k)+k(k-1)/2 [with T(2, k)=k] =T(n, k-1)+1+(n-2)(k-1) [with T(n, 0)=0] =k+(n-2)k(k-1)/2 =k+A063212(n-2, k-1) - Henry Bottomley (se16(AT)btinternet.com), Jul 11 2001
G.f. for row n: (1+(n-3)x)/(1-x)^3, n>=2. - Paul Barry (pbarry(AT)wit.ie), Feb 21 2003
|
|
EXAMPLE
|
Array (n >= 2, k >= 1) begins:
1 2 3 4 5 6 7 ...
1 3 6 10 15 21 ...
1 4 9 16 25 36 ...
1 5 12 22 35 51 ...
1 6 15 28 45 66 ...
|
|
CROSSREFS
|
Many rows and columns of this array are in the database.
Antidiagonal sums form A055795.
Sequence in context: A093430 A074659 A131251 this_sequence A134394 A074909 A135278
Adjacent sequences: A057142 A057143 A057144 this_sequence A057146 A057147 A057148
|
|
KEYWORD
|
nonn,nice,tabl,easy
|
|
AUTHOR
|
N. J. A. Sloane (njas(AT)research.att.com), Sep 12 2000
|
|
|
Search completed in 0.002 seconds
|
