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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
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
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.)