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A223399 4 X 4 square grid graph coloring a rectangular array: number of n X 5 0..15 arrays where 0..15 label nodes of the square grid graph and every array movement to a horizontal or vertical neighbor moves along an edge of this graph 1

%I

%S 1576,127464,11561512,1080643264,102163935000,9705525235832,

%T 924127826390176,88090590750261080,8401742793556003144,

%U 801551619655700687184,76481374186014708201576,7298126827012131788515624

%N 4 X 4 square grid graph coloring a rectangular array: number of n X 5 0..15 arrays where 0..15 label nodes of the square grid graph and every array movement to a horizontal or vertical neighbor moves along an edge of this graph

%C Column 5 of A223402.

%H R. H. Hardin, <a href="/A223399/b223399.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 118*a(n-1) +2145*a(n-2) -525715*a(n-3) +6093819*a(n-4) +625521315*a(n-5) -12533760928*a(n-6) -314071213351*a(n-7) +8647938684642*a(n-8) +70822768049052*a(n-9) -3054067338805723*a(n-10) -3591776245673416*a(n-11) +630129723869464309*a(n-12) -1670879348240008858*a(n-13) -80904632516100316252*a(n-14) +425436134091887146724*a(n-15) +6662201996919753057875*a(n-16) -50501387737454110362077*a(n-17) -352293141378247766724257*a(n-18) +3702654746347400267203967*a(n-19) +11288094582807812111984193*a(n-20) -183423061019271104144569287*a(n-21) -150543158457532559387455530*a(n-22) +6420922951463810201010588669*a(n-23) -4193932338511676469243368214*a(n-24) -162797268955187585369458460020*a(n-25) +289870704776031935817875930748*a(n-26) +3020660821443382995310028299773*a(n-27) -8471088004819352850334129264573*a(n-28) -40789019071457794875458679747566*a(n-29) +161768848311393656575597110164396*a(n-30) +387082671802333813322517633005275*a(n-31) -2221673076574624608220519924697188*a(n-32) -2267828007965289734956912624098638*a(n-33) +22770605730064033174187694288878459*a(n-34) +2526743667847058129446315431688624*a(n-35) -176953229657347890182508941156274475*a(n-36) +101794590574488374269398554614048600*a(n-37) +1046337012909795268367966088613922205*a(n-38) -1225503425940644964513465842312618898*a(n-39) -4667010007623544113260933655492763737*a(n-40) +8371342072143963061504850335118129923*a(n-41) +15238705634858484428173338099389725758*a(n-42) -40153915473560579439193550429671844320*a(n-43) -33254159453709192258309591312403785756*a(n-44) +143534144644882413918676586119506288691*a(n-45) +30310897924678098832181261180601393836*a(n-46) -390792342601488430891989176348089762465*a(n-47) +92195391230943615103222180851825452398*a(n-48) +814224287269911203476594013905344870366*a(n-49) -498620152910223150057690141704984776858*a(n-50) -1285769415303104876845717062059421272945*a(n-51) +1279278845441473981785207384308915417821*a(n-52) +1489278211367712606615072246950813061763*a(n-53) -2235244288643724330436967493158916651843*a(n-54) -1146608524300785363848593675548091392840*a(n-55) +2875571111747268951136886253718460232984*a(n-56) +346126181916688273915228638071220536127*a(n-57) -2789138171078918882805379414242447740771*a(n-58) +450407059318661725262536403451594846230*a(n-59) +2041724532528105517346098496599189879250*a(n-60) -818135570921782352199820062895109353198*a(n-61) -1107475511363815236876710208598775362201*a(n-62) +722443659109365249068698703578444051352*a(n-63) +422146827299609748423036558381842902409*a(n-64) -428816785522315065704598198613386133356*a(n-65) -94910904862625115727898481857813805050*a(n-66) +182941410048676687693604493419463931272*a(n-67) -364810974399022676172079172381669700*a(n-68) -56851065791838755753849801308718388908*a(n-69) +9514293925527912085642602035418453639*a(n-70) +12696721929016808651041849552943409630*a(n-71) -4030856902262277835996874644206564559*a(n-72) -1945813209767853326138128299421600769*a(n-73) +975690699465365944210030458595716868*a(n-74) +178326687930593538589330063390144536*a(n-75) -156339853089401011752402275103141200*a(n-76) -3595950677104407395906946621373952*a(n-77) +16996223208918072034063910227903036*a(n-78) -1404624678908636722588224340193912*a(n-79) -1230446923673648917317017104855520*a(n-80) +207266570820010560218111841081840*a(n-81) +55883104732540069965347507567024*a(n-82) -14762051195327931134688343452752*a(n-83) -1353909269277844627963116607456*a(n-84) +615864317621409660265398473712*a(n-85) +4907272964793154218654036608*a(n-86) -15363622694944589901806602880*a(n-87) +606866225076211480021168320*a(n-88) +220128878886246210933217920*a(n-89) -15331714873059728572743168*a(n-90) -1611762938053155019114496*a(n-91) +146624081305852532604928*a(n-92) +4355115513936939835392*a(n-93) -474826165559829823488*a(n-94) for n>95

%e Some solutions for n=3

%e .12..8..9.10.14....4..0..4..5..9....4..0..1..5..9....4..0..4..8..9

%e ..8..4..5..6.10....0..4..5..9..8....0..1..2..6..5....0..4..8..9.10

%e ..4..0..4..5..9....4..8..4..8..4....4..5..6..2..6....4..0..4..5..9

%e Vertex neighbors:

%e 0 -> 1 4

%e 1 -> 0 2 5

%e 2 -> 1 3 6

%e 3 -> 2 7

%e 4 -> 0 5 8

%e 5 -> 4 1 6 9

%e 6 -> 5 2 7 10

%e 7 -> 6 3 11

%e 8 -> 4 9 12

%e 9 -> 8 5 10 13

%e 10 -> 9 6 11 14

%e 11 -> 10 7 15

%e 12 -> 8 13

%e 13 -> 12 9 14

%e 14 -> 13 10 15

%e 15 -> 14 11

%Y Cf. A223402.

%K nonn

%O 1,1

%A _R. H. Hardin_ Mar 19 2013

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Last modified May 26 21:56 EDT 2022. Contains 354092 sequences. (Running on oeis4.)