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A053307 Number of nonnegative integer 2 X 2 matrices with sum of elements equal to n, under row and column permutations. 15
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; text; 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, Mar 17 2003
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) }. - Ramasamy Chandramouli, Jan 17 2009
These are also the "spreading numbers" alpha_4(n). See Babcock et al. for precise definition.
LINKS
B. Babcock and A. van Tuyl, Revisiting the spreading and covering numbers, arXiv preprint arXiv:1109.5847 [math.AC], 2011-2013.
John Machacek, Unique maximum independent sets in graphs on monomials of a fixed degree, arXiv:2010.11112 [math.CO], 2020.
FORMULA
G.f.: (x^2-x+1)/((1-x^2)^2*(1-x)^2).
a(n) = (n+2)*(2*n^2 + 8*n + 15 + 9*(-1)^n)/48. - Vaclav Kotesovec, Mar 16 2014
MATHEMATICA
Table[(n+2)*(2*n^2 + 8*n + 15 + 9*(-1)^n)/48, {n, 0, 20}] (* Vaclav Kotesovec, Mar 16 2014 *)
PROG
(PARI) for(n=0, 30, print1((n+2)*(2*n^2 + 8*n + 15 + 9*(-1)^n)/48, ", ")) \\ G. C. Greubel, May 31 2018
(Magma) [(n+2)*(2*n^2 + 8*n + 15 + 9*(-1)^n)/48: n in [0..30]]; // G. C. Greubel, May 31 2018
CROSSREFS
Row 2 of A318795.
Row 4 of A202175.
Sequence in context: A050018 A347513 A125577 * A076065 A176115 A066898
KEYWORD
easy,nonn
AUTHOR
Vladeta Jovovic, Mar 05 2000
STATUS
approved

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Last modified June 6 05:06 EDT 2023. Contains 363139 sequences. (Running on oeis4.)