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A053307
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Number of nonnegative integer 2 X 2 matrices with sum of elements equal to n, under row and column permutations.
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14
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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
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OFFSET
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0,3
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COMMENTS
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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.
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LINKS
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G. C. Greubel, Table of n, a(n) for n = 0..5000
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.
Index entries for linear recurrences with constant coefficients, signature (2,1,-4,1,2,-1).
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FORMULA
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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
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MATHEMATICA
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Table[(n+2)*(2*n^2 + 8*n + 15 + 9*(-1)^n)/48, {n, 0, 20}] (* Vaclav Kotesovec, Mar 16 2014 *)
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PROG
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(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
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CROSSREFS
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Row 2 of A318795.
Row 4 of A202175.
Cf. A081283, A081284.
Sequence in context: A084812 A050018 A125577 * A076065 A176115 A066898
Adjacent sequences: A053304 A053305 A053306 * A053308 A053309 A053310
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KEYWORD
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easy,nonn
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AUTHOR
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Vladeta Jovovic, Mar 05 2000
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STATUS
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approved
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