A216940 Number of side-4 hexagonal 0..n arrays with values nondecreasing E, SW and SE.

260, 27768, 1664244, 64697626, 1783839948, 37112483200, 609829326268, 8196058134921, 92610036317488, 899427798281439, 7644907607082576, 57726306147546982, 392120605767310660, 2421735824309042268

Offset

1,1

Links

R. H. Hardin, Table of n, a(n) for n = 1..37

M. Kauers and C. Koutschan, Some D-finite and some possibly D-finite sequences in the OEIS, arXiv:2303.02793 [cs.SC], 2023.

Formula

a(n) = (1+n)*(2+n)*(3+n)*(4+n)*(5+n)*(6+n)^2*(7+n)^3*(8+n)^2*(9+n)*(10+n)*(11+n)*(12+n)*(13+n)*(15118483615575730790400000 + 37557333457279933473792000*n + 45137854540680193956153600*n^2 + 34829846371335010335540480*n^3 + 19314394347459920710102704*n^4 + 8166353315859794719296864*n^5 + 2726904840964417033376520*n^6 + 735273283907306553706472*n^7 + 162382123713323392711687*n^8 + 29630015361661371290844*n^9 + 4487557575514810132362*n^10 + 564694034848365996336*n^11 + 58900361433618244860*n^12 + 5062226797216352960*n^13 + 354853893929158096*n^14 + 19969728998781072*n^15 + 880856790135603*n^16 + 29345762188932*n^17 + 694580474022*n^18 + 10413780440*n^19 + 74384146*n^20)/221424599279703105635713957232640000000 (conjectured). - Manuel Kauers and Christoph Koutschan, Mar 01 2023

Example

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

Crossrefs

Row 4 of A216937.

Sequence in context: A067639 A264162 A003734 * A395713 A200578 A383853

Adjacent sequences: A216937 A216938 A216939 * A216941 A216942 A216943

Keyword

nonn

Author

R. H. Hardin, Sep 20 2012

Status

approved