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
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