A224175 Number of 4 X n 0..3 arrays with rows, diagonals and antidiagonals unimodal and columns nondecreasing.

35, 1225, 22988, 272130, 2335459, 15925611, 91494280, 459681672, 2071283343, 8522430293, 32452346859, 115542470121, 387735671674, 1234254138386, 3746228897820, 10888055937498, 30409729685443, 81862695894551, 212957974479177, 536558013233411, 1311963232523951

Offset: 1

Author

R. H. Hardin, Mar 31 2013

Keywords

• nonn

Examples

			Some solutions for n=3:
..0..0..1....0..3..1....1..2..0....0..1..1....0..1..1....0..1..1....0..1..0
..0..2..3....3..3..1....1..3..3....0..2..2....0..1..3....1..2..1....3..1..1
..1..2..3....3..3..1....3..3..3....0..2..2....0..3..3....1..2..2....3..2..1
..2..2..3....3..3..3....3..3..3....3..2..2....2..3..3....3..3..3....3..2..2
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..210

Crossrefs

Row 4 of A224173.

Formula

Empirical: a(n) = (1/2906843957821440000)*n^24 + (1/80745665495040000)*n^23 + (40627/53523844179886080000)*n^22 + (149/6436248698880000)*n^21 + (6593077/9731608032706560000)*n^20 + (3395111/221172909834240000)*n^19 + (6648319/21341245685760000)*n^18 + (58653979/10670622842880000)*n^17 + (28432949/331085905920000)*n^16 + (2936797909/2510734786560000)*n^15 + (18556527629/1369491701760000)*n^14 + (39701629159/289700167680000)*n^13 + (122790999059713/110472330608640000)*n^12 + (19552381958779/2510734786560000)*n^11 + (343066282192637/7532204359680000)*n^10 + (2966503457023/14265538560000)*n^9 + (24242241250827793/32011868528640000)*n^8 + (16514299013828449/8002967132160000)*n^7 + (364205524025441321/152056375511040000)*n^6 + (32838681788587261/2111894104320000)*n^5 - (148032441802153/14768490240000)*n^4 - (1586985136748719/5866372512000)*n^3 + (228836377537124017/148419224553600)*n^2 - (1300791949339/411863760)*n + 2639 for n>2.

Extensions

Name corrected by Andrew Howroyd, Mar 18 2025