login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A285281 Array read by antidiagonals: T(m,n) = number of m-ary words of length n with cyclically adjacent elements differing by 3 or less. 4
1, 4, 1, 16, 5, 1, 64, 23, 6, 1, 256, 101, 30, 7, 1, 1024, 467, 138, 37, 8, 1, 4096, 2165, 694, 175, 44, 9, 1, 16384, 10055, 3526, 925, 212, 51, 10, 1, 65536, 46709, 18012, 4977, 1156, 249, 58, 11, 1, 262144, 216995, 92140, 27067, 6428, 1387, 286, 65, 12, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

4,2

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 = 4..1278

EXAMPLE

Table starts (m>=4, n>=0):

1  4 16  64  256  1024  4096  16384   65536 ...

1  5 23 101  467  2165 10055  46709  216995 ...

1  6 30 138  694  3526 18012  92140  471566 ...

1  7 37 175  925  4977 27067 147777  808165 ...

1  8 44 212 1156  6428 36338 206942 1183164 ...

1  9 51 249 1387  7879 45663 267367 1575395 ...

1 10 58 286 1618  9330 54994 328058 1973026 ...

1 11 65 323 1849 10781 64325 388749 2371457 ...

1 12 72 360 2080 12232 73656 449440 2770016 ...

MATHEMATICA

diff = 3; m0 = diff + 1; mmax = 13;

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*Sum[TransferGf[m, Boole[# == k] &, Boole[Abs[#1 - #2] <= d] &, Boole[Abs[# - k] <= d] &, z], {k, 1, m}];

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 16 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*sum(k=1, m, TransferGf(m, i->if(i==k, 1, 0), (i, j)->abs(i-j)<=d, j->if(abs(j-k)<=d, 1, 0), z));

for(m=4, 12, print(RowGf(3, m, x)));

for(m=4, 12, v=Vec(RowGf(3, m, x) + O(x^9)); for(n=1, length(v), print1( v[n], ", ") ); print(); );

CROSSREFS

Rows 5-32 are A124999, A125316-A125342.

Cf. A285267, A285280, A276562.

Sequence in context: A167343 A094361 A187926 * A285267 A067425 A188481

Adjacent sequences:  A285278 A285279 A285280 * A285282 A285283 A285284

KEYWORD

nonn,tabl

AUTHOR

Andrew Howroyd, Apr 15 2017

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 3 05:05 EST 2021. Contains 349445 sequences. (Running on oeis4.)