A264946 Number of 3 X n arrays containing n copies of 0..3-1 with no equal horizontal neighbors and new values introduced sequentially from 0.

1, 8, 56, 332, 2350, 16108, 114148, 817280, 5918424, 43251920, 318428920, 2359455400, 17577965926, 131579085320, 989014916960, 7461197116280, 56471149527616, 428656384570808, 3262347081071272, 24887490475059512

Offset

1,2

Comments

Row 3 of A264945.

Links

R. H. Hardin, Table of n, a(n) for n = 1..104

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

Formula

Conjectured recurrence of order 9 and degree 13: (n + 7)*(n + 9)*(n + 11)*(n + 12)*(1125*n^9 + 71100*n^8 + 1849290*n^7 + 25782456*n^6 + 208721101*n^5 + 972463852*n^4 + 2219593700*n^3 + 50298752*n^2 - 10311481536*n - 14857032960)*a(n + 9) - (n + 8)*(n + 11)*(1125*n^11 + 105975*n^10 + 4287165*n^9 + 97635351*n^8 + 1380358747*n^7 + 12566316081*n^6 + 73253605103*n^5 + 255547606333*n^4 + 398433897060*n^3 - 409020958588*n^2 - 2573789550288*n - 2893020641280)*a(n + 8) - (n + 7)*(55125*n^12 + 5043150*n^11 + 203593785*n^10 + 4783109874*n^9 + 72494563771*n^8 + 740695604282*n^7 + 5151899227595*n^6 + 23797245731102*n^5 + 66502991649164*n^4 + 73821686951912*n^3 - 148787634331808*n^2 - 594255830565888*n - 585045220193280)*a(n + 7) + (-111375*n^13 - 10629900*n^12 - 452242260*n^11 - 11349359364*n^10 - 187042020462*n^9 - 2127929201500*n^8 - 17043729555112*n^7 - 95651673757276*n^6 - 362118971182795*n^5 - 819923758737640*n^4 - 569404973885116*n^3 + 2298397321892016*n^2 + 6690359386550016*n + 5779315376271360)*a(n + 6) + 4*(68625*n^13 + 6350850*n^12 + 262268790*n^11 + 6397257006*n^10 + 102643250092*n^9 + 1138907266426*n^8 + 8907524302014*n^7 + 48769985579898*n^6 + 178866084976275*n^5 + 380439835948764*n^4 + 162302253918524*n^3 - 1409022793603840*n^2 - 3584273436805056*n - 2901502849512960)*a(n + 5) + 8*(113625*n^13 + 10109475*n^12 + 400010115*n^11 + 9340598391*n^10 + 143726469497*n^9 + 1536021852345*n^8 + 11649644036681*n^7 + 62442624371309*n^6 + 227373943553018*n^5 + 494618567601008*n^4 + 295071232164264*n^3 - 1523160592469296*n^2 - 4224581839405248*n - 3597712690682880)*a(n + 4) + 16*(10125*n^13 + 791775*n^12 + 27734085*n^11 + 599490219*n^10 + 9285055875*n^9 + 110260636645*n^8 + 1005826848007*n^7 + 6794028883657*n^6 + 32142152171668*n^5 + 97251455731576*n^4 + 145564079336272*n^3 - 68830984119216*n^2 - 616978454170176*n - 699609347458560)*a(n + 3) - 16*(102375*n^13 + 8429850*n^12 + 302519490*n^11 + 6252315786*n^10 + 82728789292*n^9 + 735119632054*n^8 + 4454619907050*n^7 + 18120079094814*n^6 + 45886145527965*n^5 + 51009713975544*n^4 - 78118093654492*n^3 - 396941915101552*n^2 - 632960801821824*n - 397766739363840)*a(n + 2) - 64*(n + 1)*(28125*n^11 + 2145375*n^10 + 69983925*n^9 + 1286257695*n^8 + 14737434403*n^7 + 109491713225*n^6 + 526473720215*n^5 + 1544097805013*n^4 + 2140227079172*n^3 - 1382380121116*n^2 - 9705594256208*n - 11040556116480)*n*a(n + 1) - 512*(n - 1)*(n + 1)*(1125*n^9 + 81225*n^8 + 2458590*n^7 + 40812786*n^6 + 406374277*n^5 + 2472650097*n^4 + 8781110488*n^3 + 15058677204*n^2 + 1549576672*n - 21689733120)*n^2*a(n) = 0. - Manuel Kauers and Christoph Koutschan, Mar 06 2023

Conjecture: a(n) ~ 3^(7/2) * 2^(3*n - 5) / (Pi*n), based on the recurrence by Manuel Kauers and Christoph Koutschan. - Vaclav Kotesovec, Mar 07 2023

Example

Some solutions for n=4:
  0 1 2 1    0 1 0 1    0 1 0 2    0 1 2 1    0 1 2 0
  1 0 2 0    0 2 1 2    1 0 2 1    2 0 2 1    0 2 1 2
  1 2 0 2    2 0 2 1    2 0 1 2    1 0 2 0    1 0 1 2

Crossrefs

Cf. A264945.

Sequence in context: A336906 A334332 A068552 * A319891 A319872 A215227

Adjacent sequences: A264943 A264944 A264945 * A264947 A264948 A264949

Keyword

nonn

Author

R. H. Hardin, Nov 29 2015

Status

approved