A340648 a(n) is the maximum number of nonzero entries in an n X n sign-restricted matrix.
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
Offset: 0
Links
- 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).
Crossrefs
Cf. A225231.
Programs
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Mathematica
LinearRecurrence[{3, -4, 4, -3, 1}, {0, 1, 3, 6, 11}, 50] (* Amiram Eldar, Jan 14 2021 *) -
PARI
a(n) = my(x=n % 4); if ((x==0) || (x==3), (3*n^2-n)/4, (3*n^2-n+2)/4);
Formula
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
Comments