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

0,2

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