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, 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

Offset: 0

Author

Yukun Yao, Feb 11 2019

Keywords

• nonn

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.

Examples

			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.
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..1000
• Doron Zeilberger, Experimental Mathematics Class in Spring 2019, C6.txt; Local copy

Programs

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

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.

Extensions

a(0)=1 prepended and terms a(11) and beyond from Andrew Howroyd, Mar 01 2020