A204880 Number of (n+2) X 3 0..3 arrays with every 3 X 3 subblock having three equal elements in a row horizontally, vertically or nw-to-se diagonally exactly one way, and new values 0..3 introduced in row major order.

3348, 91703, 2604782, 61994345, 1609422202, 43272008917, 1093785287286, 28171869515568, 739117052027915, 19015612616935859, 490455315815506569, 12749198525042431006, 329530231007321036517, 8513765514392601907380

Offset

1,1

Comments

Column 1 of A204884.

Links

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

Formula

Empirical: a(n) = 21*a(n-1) +41*a(n-2) +5956*a(n-3) -85399*a(n-4) -571671*a(n-5) +5746493*a(n-6) +38113234*a(n-7) -109469317*a(n-8) -1609753913*a(n-9) -2190299685*a(n-10) +31312264804*a(n-11) +147518016342*a(n-12) -128445838170*a(n-13) -2974271197697*a(n-14) -4641165047679*a(n-15) +27361002602986*a(n-16) +84231288799387*a(n-17) -118013048926211*a(n-18) -730255999037406*a(n-19) +494614648616336*a(n-20) +4781329076777116*a(n-21) -4305828883739700*a(n-22) -29040024909616240*a(n-23) +11939404196138785*a(n-24) +129458871076161445*a(n-25) +204725659695717740*a(n-26) -486151119759854565*a(n-27) -1780947787725525750*a(n-28) +2541856755237534547*a(n-29) +379329934589385724*a(n-30) +3448943191595078683*a(n-31) +8560512850871041932*a(n-32) -52087328831538029883*a(n-33) +73498292332650743820*a(n-34) -117564387597986894927*a(n-35) +154511150901340232576*a(n-36) +158105762642110223751*a(n-37) -794166021655563243807*a(n-38) +1449915664894316999226*a(n-39) -2319497198395279774758*a(n-40) +3152395853326042811820*a(n-41) -3077159238342032332734*a(n-42) +1851051999171023409168*a(n-43) +1012814819239670502588*a(n-44) -6368974164984089334024*a(n-45) +11826741075974474904936*a(n-46) -14555479659385494171888*a(n-47) +21341511527210866337184*a(n-48) -40640163454936767954528*a(n-49) +64179057397487705467776*a(n-50) -72922922509983846771456*a(n-51) +56627319891732020917056*a(n-52) -24712517615962005492480*a(n-53) -1953405055188430456320*a(n-54) +12342207734650220009472*a(n-55) -9765649174347976485888*a(n-56) +2984537641774792568832*a(n-57) +333290808043194138624*a(n-58) +257420137499091468288*a(n-59) -726013334319058649088*a(n-60) +256662322492420915200*a(n-61) -8423789045905096704*a(n-62) for n>63.

Example

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

Crossrefs

Sequence in context: A348525 A255731 A204884 * A151601 A251817 A216488

Adjacent sequences: A204877 A204878 A204879 * A204881 A204882 A204883

Keyword

nonn

Author

R. H. Hardin, Jan 20 2012

Status

approved