This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A285280 Array read by antidiagonals: T(m,n) = number of m-ary words of length n with cyclically adjacent elements differing by 2 or less. 4
 1, 3, 1, 9, 4, 1, 27, 14, 5, 1, 81, 46, 19, 6, 1, 243, 162, 65, 24, 7, 1, 729, 574, 247, 84, 29, 8, 1, 2187, 2042, 955, 332, 103, 34, 9, 1, 6561, 7270, 3733, 1336, 417, 122, 39, 10, 1, 19683, 25890, 14649, 5478, 1717, 502, 141, 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 Table starts (m>=3, n>=0): 1  3  9  27  81  243   729  2187 ... 1  4 14  46 162  574  2042  7270 ... 1  5 19  65 247  955  3733 14649 ... 1  6 24  84 332 1336  5478 22658 ... 1  7 29 103 417 1717  7229 30793 ... 1  8 34 122 502 2098  8980 38928 ... 1  9 39 141 587 2479 10731 47063 ... 1 10 44 160 672 2860 12482 55198 ... MATHEMATICA diff = 2; m0 = diff + 1; 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*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=3, 10, print(RowGf(2, m, x))); for(m=3, 10, v=Vec(RowGf(2, m, x) + O(x^8)); for(n=1, length(v), print1( v[n], ", ") ); print(); ); CROSSREFS Rows 4-32 are A124805, A124806, A124807, A124828, A124843, A124851, A124852, A124857, A124858, A124864, A124892-A124894, A124898, A124935, A124947, A124948-A124958, A124994, A124998. Cf. A285266, A276562, A285281. Sequence in context: A054448 A106516 A140071 * A285266 A067417 A187887 Adjacent sequences:  A285277 A285278 A285279 * A285281 A285282 A285283 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.

Last modified February 22 18:05 EST 2019. Contains 320400 sequences. (Running on oeis4.)