cp's OEIS Frontend

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.

%I A264946 #17 Mar 07 2023 02:44:27
%S A264946 1,8,56,332,2350,16108,114148,817280,5918424,43251920,318428920,
%T A264946 2359455400,17577965926,131579085320,989014916960,7461197116280,
%U A264946 56471149527616,428656384570808,3262347081071272,24887490475059512
%N 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.
%C A264946 Row 3 of A264945.
%H A264946 R. H. Hardin, <a href="/A264946/b264946.txt">Table of n, a(n) for n = 1..104</a>
%H A264946 M. Kauers and C. Koutschan, <a href="https://arxiv.org/abs/2303.02793">Some D-finite and some possibly D-finite sequences in the OEIS</a>, arXiv:2303.02793 [cs.SC], 2023.
%F A264946 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
%F A264946 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
%e A264946 Some solutions for n=4:
%e A264946   0 1 2 1    0 1 0 1    0 1 0 2    0 1 2 1    0 1 2 0
%e A264946   1 0 2 0    0 2 1 2    1 0 2 1    2 0 2 1    0 2 1 2
%e A264946   1 2 0 2    2 0 2 1    2 0 1 2    1 0 2 0    1 0 1 2
%Y A264946 Cf. A264945.
%K A264946 nonn
%O A264946 1,2
%A A264946 _R. H. Hardin_, Nov 29 2015