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A340648
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a(n) is the maximum number of nonzero entries in an n X n sign-restricted matrix.
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0
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0, 1, 3, 6, 11, 18, 26, 35, 46, 59, 73, 88, 105, 124, 144, 165, 188, 213, 239, 266, 295, 326, 358, 391, 426, 463, 501, 540, 581, 624, 668, 713, 760, 809, 859, 910, 963, 1018, 1074, 1131, 1190, 1251, 1313, 1376, 1441, 1508, 1576, 1645, 1716, 1789, 1863, 1938, 2015
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OFFSET
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0,3
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COMMENTS
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A sign-restricted matrix is such that each partial column sum, starting from row 1, equals 0 or 1, and each partial row sum, starting from column 1, is nonnegative.
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LINKS
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Table of n, a(n) for n=0..52.
Richard A. Brualdi and Geir Dahl, Sign-restricted matrices of 0's, 1's, and -1's, arXiv:2101.04150 [math.CO], 2021.
Index entries for linear recurrences with constant coefficients, signature (3,-4,4,-3,1).
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FORMULA
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a(n) = (3*n^2-n)/4 if (n==0) or (n==3) (mod 4);
a(n) = (3*n^2-n+2)/4 if (n==1) or (n==2) (mod 4).
From Stefano Spezia, Jan 14 2021: (Start)
G.f.: x*(1 + x^2 + x^3)/((1 - x)^3*(1 + x^2)).
a(n) = 3*a(n-1) - 4*a(n-2) + 4*a(n-3) - 3*a(n-4) + a(n-5) for n > 4. (End)
For n >= 4, a(n) = (A225231(n+1) + 1)/2 - 1. - Hugo Pfoertner, Jan 17 2021
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MATHEMATICA
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LinearRecurrence[{3, -4, 4, -3, 1}, {0, 1, 3, 6, 11}, 50] (* Amiram Eldar, Jan 14 2021 *)
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PROG
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(PARI) a(n) = my(x=n % 4); if ((x==0) || (x==3), (3*n^2-n)/4, (3*n^2-n+2)/4);
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CROSSREFS
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Cf. A225231.
Sequence in context: A084576 A024667 A025210 * A140126 A140235 A224214
Adjacent sequences: A340645 A340646 A340647 * A340649 A340650 A340651
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KEYWORD
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nonn,easy
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AUTHOR
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Michel Marcus, Jan 14 2021
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STATUS
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approved
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