OFFSET
3,2
COMMENTS
All rows are linear recurrences with constant coefficients. See PARI script to obtain generating functions.
LINKS
Andrew Howroyd, Table of n, a(n) for n = 3..1277
EXAMPLE
Array starts (m>=3, n>=0):
1 3 9 27 81 243 729 2187 6561 ...
1 4 14 50 178 634 2258 8042 28642 ...
1 5 19 75 295 1161 4569 17981 70763 ...
1 6 24 100 418 1748 7310 30570 127842 ...
1 7 29 125 543 2363 10287 44787 194995 ...
1 8 34 150 668 2986 13362 59816 267802 ...
1 9 39 175 793 3611 16475 75229 343633 ...
1 10 44 200 918 4236 19598 90790 420870 ...
MATHEMATICA
diff = 2; m0 = 3; mmax = 12;
TransferGf[m_, u_, t_, v_, z_] := Array[u, m].LinearSolve[IdentityMatrix[m] - z*Array[t, {m, m}], Array[v, m]]
RowGf[d_, m_, z_] := 1+z*TransferGf[m, 1&, Boole[Abs[#1-#2] <= d]&, 1&, z];
row[m_] := row[m] = CoefficientList[RowGf[diff, m, x] + O[x]^mmax, x];
T[m_ /; m >= m0, n_ /; n >= 0] := row[m][[n + 1]];
Table[T[m - n , n], {m, m0, mmax}, {n, m - m0, 0, -1}] // Flatten (* Jean-François Alcover, Jun 17 2017, adapted from PARI *)
PROG
(PARI)
TransferGf(m, u, t, v, z)=vector(m, i, u(i))*matsolve(matid(m)-z*matrix(m, m, i, j, t(i, j)), vectorv(m, i, v(i)));
RowGf(d, m, z)=1+z*TransferGf(m, i->1, (i, j)->abs(i-j)<=d, j->1, z);
for(m=3, 10, print(RowGf(2, m, x)));
for(m=3, 10, v=Vec(RowGf(2, m, x) + O(x^9)); for(n=1, length(v), print1( v[n], ", ") ); print(); );
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Andrew Howroyd, Apr 15 2017
STATUS
approved