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A285266 Array read by antidiagonals: T(m,n) = number of m-ary words of length n with adjacent elements differing by 2 or less. 3
1, 3, 1, 9, 4, 1, 27, 14, 5, 1, 81, 50, 19, 6, 1, 243, 178, 75, 24, 7, 1, 729, 634, 295, 100, 29, 8, 1, 2187, 2258, 1161, 418, 125, 34, 9, 1, 6561, 8042, 4569, 1748, 543, 150, 39, 10, 1, 19683, 28642, 17981, 7310, 2363, 668, 175, 44, 11, 1 (list; table; graph; refs; listen; history; text; internal format)
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-Fran├žois 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

Rows 4-32 are A055099, A126392-A126419.

Cf. A285280, A188866, A285267.

Sequence in context: A106516 A140071 A285280 * A067417 A187887 A016577

Adjacent sequences:  A285263 A285264 A285265 * A285267 A285268 A285269

KEYWORD

nonn,tabl

AUTHOR

Andrew Howroyd, Apr 15 2017

STATUS

approved

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Last modified February 19 07:51 EST 2019. Contains 320309 sequences. (Running on oeis4.)