|
Search: id:A107379
|
|
|
| A107379 |
|
Number of ways to write n^2 as the sum of n odd numbers, disregarding order. |
|
+0
4
|
|
| 1, 1, 3, 9, 30, 110, 436, 1801, 7657, 33401, 148847, 674585, 3100410, 14422567, 67792847, 321546251, 1537241148, 7400926549, 35854579015, 174677578889, 855312650751, 4207291811538, 20782253017825, 103048079556241
(list; graph; listen)
|
|
|
OFFSET
|
0,3
|
|
|
COMMENT
|
Motivated by the fact that the nth square is equal to the sum of the first n odd numbers.
|
|
FORMULA
|
a(n) = A008284((n^2+n)/2,n) = A008284(A000217(n),n). - Max Alekseyev, Sep 25 2009
|
|
EXAMPLE
|
For example, 9 can be written as a sum of three odd numbers in 3 ways: 1+1+7, 1+3+5 and 3+3+3.
|
|
MAPLE
|
f := proc (n, k) option remember;
if n = 0 and k = 0 then return 1 end if;
if n <= 0 or n < k then return 0 end if;
if `mod`(n+k, 2) = 1 then return 0 end if;
if k = 1 then return 1 end if;
return f(n-1, k-1) + f(n-2*k, k)
end proc;
seq(f(k^2, k), k=1..20);
|
|
CROSSREFS
|
Cf. A152140.
Sequence in context: A091699 A129167 A151472 this_sequence A117428 A134168 A124427
Adjacent sequences: A107376 A107377 A107378 this_sequence A107380 A107381 A107382
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
David Radcliffe (dradcliffe(AT)gmail.com), Sep 25 2009
|
|
EXTENSIONS
|
Arguments in the Maple program swapped and 4 terms added by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 02 2009
|
|
|
Search completed in 0.002 seconds
|
