A278604 Number of n X 1 0..3 arrays with rows and columns in lexicographic nondecreasing order but with exactly three mistakes.

0, 0, 0, 1, 56, 728, 5328, 27876, 116304, 411334, 1281280, 3606980, 9346624, 22597760, 51507280, 111578412, 231211152, 460720740, 886647920, 1653955415, 2999760280, 5303659240, 9161558720, 15492338160, 25689792960, 41836287690, 66999597840, 105640761810

Offset

1,5

Links

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

Index entries for linear recurrences with constant coefficients, signature (16,-120,560,-1820,4368,-8008,11440,-12870,11440,-8008,4368,-1820,560,-120,16,-1).

Formula

a(n) = (1/1307674368000)*n^15 + (1/10897286400)*n^14 + (47/9340531200)*n^13 + (17/119750400)*n^12 + (193/93312000)*n^11 + (37/3628800)*n^10 - (26401/457228800)*n^9 - (47183/76204800)*n^8 + (1918993/1306368000)*n^7 + (3793/544320)*n^6 - (386327/25660800)*n^5 - (151381/6652800)*n^4 + (441553891/9081072000)*n^3 + (275711/16816800)*n^2 - (191/5460)*n.

a(n) = A008287(n+1,15) = C(n+15,15) - (n+1)*C(n+11,11) + C(n+1,2)*C(n+7,7) - C(n+1,3)*C(n+3,3). - Mathew Englander, May 19 2026

G.f.: x^4*(10*x^8-80*x^7+270*x^6-480*x^5+448*x^4-160*x^3-48*x^2+40*x+1)/(x-1)^16. - Alois P. Heinz, May 19 2026

Example

Some solutions for n=6
..2. .2. .2. .3. .3. .2. .3. .0. .1. .1. .2. .2. .2. .3. .3. .3
..1. .1. .1. .2. .2. .1. .1. .3. .2. .2. .1. .0. .1. .0. .2. .2
..0. .1. .2. .3. .0. .0. .2. .2. .1. .0. .1. .1. .0. .2. .1. .3
..2. .3. .1. .1. .0. .1. .1. .1. .0. .3. .3. .0. .3. .1. .2. .1
..0. .2. .3. .0. .3. .3. .0. .3. .2. .2. .2. .2. .1. .3. .1. .3
..1. .0. .0. .2. .2. .0. .0. .0. .1. .1. .1. .0. .2. .0. .3. .1

Crossrefs

Column 1 of A278610.

Cf. A008287.

Sequence in context: A136006 A138410 A240269 * A201098 A190419 A105940

Adjacent sequences: A278601 A278602 A278603 * A278605 A278606 A278607

Keyword

nonn,easy

Author

R. H. Hardin, Nov 23 2016

Status

approved