A266103 - OEIS

%I #10 Oct 11 2023 15:52:14

%S 1,16,64,161,736,3846,16103,62778,274466,1238762,5293041,22276043,

%T 96335136,419550430,1803305352,7726652568,33323635453,143929545318,

%U 619694522447,2666428933331,11491110825839,49536410438938

%N Number of 3 X n integer arrays with each element equal to the number of horizontal and antidiagonal neighbors exactly one smaller than itself.

%C Row 3 of A266101.

%H R. H. Hardin, <a href="/A266103/b266103.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 4*a(n-1) +10*a(n-3) +60*a(n-4) -241*a(n-5) -275*a(n-6) -275*a(n-7) -1906*a(n-8) +266*a(n-10) +23553*a(n-11) +69768*a(n-12) -50662*a(n-13) -109039*a(n-14) -248005*a(n-15) -977832*a(n-16) +907466*a(n-17) +5373976*a(n-18) +8491160*a(n-19) +9435986*a(n-20) +1644865*a(n-21) -7010416*a(n-22) -13190485*a(n-23) -19551301*a(n-24) -9946324*a(n-25) -6037790*a(n-26) +3234342*a(n-27) +10883758*a(n-28) -1052994*a(n-29) +7949179*a(n-30) -1563048*a(n-31) +1098828*a(n-32) +11920090*a(n-33) +5977957*a(n-34) +20415705*a(n-35) +3449370*a(n-36) -7285989*a(n-37) -8698518*a(n-38) -13671771*a(n-39) -4863001*a(n-40) -5896817*a(n-41) -1867155*a(n-42) +2201749*a(n-43) +3172499*a(n-44) +3923456*a(n-45) +1976757*a(n-46) +1117259*a(n-47) +326318*a(n-48) -477791*a(n-49) -602510*a(n-50) -384845*a(n-51) -145647*a(n-52) -80645*a(n-53) -45723*a(n-54) +11145*a(n-55) +31554*a(n-56) +13446*a(n-57) +4398*a(n-58) +2741*a(n-59) -52*a(n-60) -526*a(n-61) -71*a(n-62) +19*a(n-63) +3*a(n-64) for n>68.

%e Some solutions for n=4:

%e ..1..0..1..1....1..0..0..0....0..0..0..0....0..0..0..1....1..0..1..2

%e ..0..2..0..0....0..0..2..1....1..2..0..0....0..0..1..1....0..2..1..1

%e ..1..0..0..1....1..1..0..0....1..0..0..0....1..2..0..0....0..0..0..0

%Y Cf. A266101.

%K nonn

%O 1,2

%A _R. H. Hardin_, Dec 21 2015