A196714 Number of nX4 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 4,0,2,1,3 for x=0,1,2,3,4

5, 36, 171, 1142, 6078, 36590, 222112, 1307674, 7735880, 45646026, 269504078, 1595690953, 9445961529, 55865469801, 330371020703, 1953941440845, 11557262522313, 68362216702686, 404360196543732, 2391711672587354

Offset

1,1

Comments

Every 0 is next to 0 4's, every 1 is next to 1 0's, every 2 is next to 2 2's, every 3 is next to 3 1's, every 4 is next to 4 3's

Column 4 of A196718

Links

R. H. Hardin, Table of n, a(n) for n = 1..200

Formula

Empirical: a(n) = 8*a(n-1) -16*a(n-2) +33*a(n-3) -44*a(n-4) +197*a(n-5) -1314*a(n-6) -3675*a(n-7) -4069*a(n-8) +8994*a(n-9) -6311*a(n-10) +130127*a(n-11) +932622*a(n-12) +1290609*a(n-13) +2010374*a(n-14) +5442198*a(n-15) -3445933*a(n-16) -26829543*a(n-17) -95381098*a(n-18) -376159657*a(n-19) -888672107*a(n-20) -886091315*a(n-21) -1045213530*a(n-22) +942081668*a(n-23) +10394295602*a(n-24) +19998310165*a(n-25) +45667424668*a(n-26) +57280962709*a(n-27) +28022306969*a(n-28) +29329870916*a(n-29) +74905152085*a(n-30) +339364993521*a(n-31) +534264439140*a(n-32) +345936449526*a(n-33) +59667367834*a(n-34) +91201347050*a(n-35) +1038145942768*a(n-36) +1277689242644*a(n-37) -1099010534855*a(n-38) -4907426601589*a(n-39) -6126737363462*a(n-40) -2773973022744*a(n-41) +185766823358*a(n-42) -3272648129811*a(n-43) -11067381090042*a(n-44) -12559905118605*a(n-45) -9867830305957*a(n-46) -16609179704277*a(n-47) -18276877080354*a(n-48) +1168018847975*a(n-49) +21179347931697*a(n-50) +24360110709872*a(n-51) +20944118386052*a(n-52) +11647836882502*a(n-53) -3281064242330*a(n-54) -7208105283807*a(n-55) -2819397124311*a(n-56) +366702878518*a(n-57) +3519213054787*a(n-58) +5891894894118*a(n-59) +4059679915511*a(n-60) +480674016410*a(n-61) -1979647698761*a(n-62) -2275683181549*a(n-63) -879268829250*a(n-64) -35733241634*a(n-65) +449450577395*a(n-66) +422581246796*a(n-67) +12127855224*a(n-68) +5499286477*a(n-69) +22280050236*a(n-70) -113151659412*a(n-71) -91555982797*a(n-72) +43253463185*a(n-73) +65906627671*a(n-74) -8407724914*a(n-75) -22765288071*a(n-76) +2530625488*a(n-77) +7972121475*a(n-78) -685107627*a(n-79) -3790263396*a(n-80) -200981550*a(n-81) +1097049596*a(n-82) +294203436*a(n-83) -171721608*a(n-84) -87006899*a(n-85) +6177016*a(n-86) +12337054*a(n-87) +1948440*a(n-88) -555373*a(n-89) -135110*a(n-90) -36892*a(n-91) -7162*a(n-92) -1989*a(n-93) -242*a(n-94) +32*a(n-95) for n>97

Example

Some solutions for n=5
..1..1..0..1....2..2..0..0....0..1..3..1....0..1..1..0....2..2..0..0
..0..1..2..2....2..2..0..0....0..1..1..0....1..2..2..2....2..2..0..0
..1..1..2..2....1..0..0..0....0..3..1..0....1..2..0..2....0..1..1..1
..1..0..0..0....1..0..0..0....0..1..1..1....0..2..1..2....2..2..1..1
..1..0..0..0....1..0..0..0....1..1..0..1....1..2..2..2....2..2..0..0

Crossrefs

Sequence in context: A109726 A272561 A266097 * A048535 A272150 A271254

Adjacent sequences: A196711 A196712 A196713 * A196715 A196716 A196717

Keyword

nonn

Author

R. H. Hardin Oct 05 2011

Status

approved