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 A306381 a(n) is the number of semimagic 4 X 3 matrices whose entries are nonnegative integers, with row sum = 3*n and column sum = 4*n. 1
 1, 415, 8623, 64405, 289981, 965071, 2626975, 6195673, 13123945, 25572511, 46610191, 80439085, 132644773, 210471535, 323122591, 482085361, 701481745, 998443423, 1393512175, 1911065221, 2579765581, 3433037455, 4509566623, 5853825865, 7516625401, 9555688351 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS This sequence was found during Doron Zeilberger's Experimental Mathematics class on Feb. 11, 2019. All class members contributed to the discovery of this sequence. LINKS Andrew Howroyd, Table of n, a(n) for n = 0..1000 Doron Zeilberger, Experimental Mathematics Class in Spring 2019, C6.txt; Local copy FORMULA a(n) = (139/4)*n^6 + (417/4)*n^5 + (535/4)*n^4 + (375/4)*n^3 + (77/2)*n^2 + 9*n + 1. EXAMPLE For n=1 the a(1)= 415 because there are 415 4 X 3 matrices with nonnegative integer entries, whose row sum is 3 and column sum is 4. PROG (PARI) a(n) = {(139*n^6 + 417*n^5 + 535*n^4 + 375*n^3 + 154*n^2 + 36*n + 4)/4} \\ Andrew Howroyd, Mar 01 2020 CROSSREFS Sequence in context: A184545 A096032 A166057 * A172779 A056068 A224602 Adjacent sequences: A306378 A306379 A306380 * A306382 A306383 A306384 KEYWORD nonn AUTHOR Yukun Yao, Feb 11 2019 EXTENSIONS a(0)=1 prepended and terms a(11) and beyond from Andrew Howroyd, Mar 01 2020 STATUS approved

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Last modified June 21 18:40 EDT 2024. Contains 373556 sequences. (Running on oeis4.)