|
| |
|
|
A053307
|
|
Number of nonnegative integer 2 X 2 matrices with sum of elements equal to n, under row and column permutations.
|
|
10
| |
|
|
1, 1, 4, 5, 11, 14, 24, 30, 45, 55, 76, 91, 119, 140, 176, 204, 249, 285, 340, 385, 451, 506, 584, 650, 741, 819, 924, 1015, 1135, 1240, 1376, 1496, 1649, 1785, 1956, 2109, 2299, 2470, 2680, 2870, 3101, 3311, 3564, 3795, 4071, 4324, 4624, 4900, 5225, 5525
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,3
|
|
|
COMMENTS
| An interleaved sequence of pyramidal and polygonal numbers: a(2n)= A006527(n+1), a(2n+1)=A000330(n+1) - Paul Barry (pbarry(AT)wit.ie), Mar 17 2003
Contribution from Ramasamy Chandramouli (thedavinci(AT)gmail.com), Jan 17 2009: a(n) is also the number of solutions to the equation XOR(x1, x2, ..., xn) = 0 such that each xi is a 2-bit binary number and xi >= xj for i >= j. For example, a(2) = 4 since (x1, x2) = { (00, 00), (01, 01), (10, 10), (11, 11) }.
These are also the "spreading numbers" alpha_4(n). See Babcock et al. for precise definition.
|
|
|
REFERENCES
| B. Babcock and A. van Tuyl, Revisiting the spreading and covering numbers, Arxiv preprint arXiv:1109.5847, 2011
|
|
|
FORMULA
| G.f.: (x^2-x+1)/((1-x^2)^2*(1-x)^2).
|
|
|
CROSSREFS
| Cf. A081283, A081284. A row of the array in A202175.
Sequence in context: A084812 A050018 A125577 * A076065 A176115 A066898
Adjacent sequences: A053304 A053305 A053306 * A053308 A053309 A053310
|
|
|
KEYWORD
| easy,nonn
|
|
|
AUTHOR
| Vladeta Jovovic (vladeta(AT)eunet.rs), Mar 05 2000
|
| |
|
|
