\\ * * * * * * * * * * * * * * * \\ coordination sequence library \\ * * * * * * * * * * * * * * * width = -1 height = -1 coord = matrix(0,0) labels = matrix(0,0) init(screen) = { height = #screen; width = #screen[1]; coord = matrix(width, height, x, y, []); labels = matrix(width, height, x, y, ""); for (s=1, #screen, my (y=#screen - s); my (row = Vec(screen[s])); for (x=0, #row-1, my (d = row[x+1]); if ( (d >= "A" && d <= "Z") || (d >= "a" && d <= "Z") || (d >= "0" && d <= "9"), eval(Str("p" d "=" x+I*y)); labels[1+x, 1+y] = d; ); ); ); } up (z) = z + I*height down (z) = z - I*height right(z) = z + width left (z) = z - width \\ unidirectional link link1(z, zz) = { my (x=real(z) % width, y=imag(z) % height); coord[1+x, 1+y] = concat(coord[1+x, 1+y], zz-z); } \\ bidirectional link link(a, b) = link1(a, b); link1(b, a); \\ bidirectional links from same origin links(a, bb) = for (i=1, #bb, link(a, bb[i])); \\ neighbours neighbours(z) = { my (x=real(z) % width, y=imag(z) % height); my (n = apply (c -> c + z, coord[1+x, 1+y])); \\ print ("#" z " -> " n); return (n); } \\ complex see/seen routines big limit = 100 000 big values = Set([]) small values = vector(4, i, []) see index(z) = { my (s=1, x=real(z), y=imag(z)); if (x<1, s += 1; x = 1-x; ); if (y<0, s += 2; y = -y; ); return ([s,x,y]); } see(z) = { my (index = see index(z)); if (max(index[2],index[3]) > big limit, big values = set union(big values, Set([z])), if (#small values[index[1]] < index[2], small values[index[1]] = concat(small values[index[1]], vector(index[2] - #small values[index[1]])) ); small values[index[1]][index[2]] = bit or(small values[index[1]][index[2]], 2^index[3]) ); } seen(z) = { my (index = see index(z)); if (max(index[2],index[3]) > big limit, return (set search(big values, z)), if (#small values[index[1]] < index[2], return (0), return (bit test(small values[index[1]][index[2]], index[3])) ); ); } \\ compute coordination sequence compute(z, mx) = { my (current = [z]); for (n=0, mx, \\ print ("#" current); print (n " " #current); if (n==mx, break); for (c=1, #current, see(current[c]); ); my (others = concat(apply(neighbours, current))); current = select(p -> !seen(p), Set(others)); ); } { \\ https://oeis.org/A316316 \\ https://oeis.org/A316317 init([ "C.........", "..........", ".....H....", "B...E.I...", ".....G....", "..........", "A.........", ".D...F...J" ]); links(pA, [ pB, pD, left(pJ) ]); links(pB, [ pC, pE, left(pI) ]); links(pC, [ up(pD), up(left(pJ)) ]); links(pD, [ pF ]); links(pE, [ pG, pH ]); links(pF, [ pG, down(pH), pJ ]); links(pG, [ pI ]); links(pH, [ pI ]); } allocatemem(2^30); compute(pB, 5 000); quit