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
Keywords
Examples
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
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.
Crossrefs
Cf. A264945.
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
Comments