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 A340648 a(n) is the maximum number of nonzero entries in an n X n sign-restricted matrix. 0
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS 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. LINKS 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). 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 MATHEMATICA LinearRecurrence[{3, -4, 4, -3, 1}, {0, 1, 3, 6, 11}, 50] (* Amiram Eldar, Jan 14 2021 *) PROG (PARI) a(n) = my(x=n % 4); if ((x==0) || (x==3), (3*n^2-n)/4, (3*n^2-n+2)/4); CROSSREFS Cf. A225231. Sequence in context: A024667 A363056 A025210 * A140126 A140235 A224214 Adjacent sequences: A340645 A340646 A340647 * A340649 A340650 A340651 KEYWORD nonn,easy AUTHOR Michel Marcus, Jan 14 2021 STATUS approved

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