OFFSET
1,6
REFERENCES
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
Bau-Sen Du, The Minimal Number of Periodic Orbits of Periods Guaranteed in Sharkovskii's Theorem. Bull. Austral. Math. Soc. 31(1985), 89-103. Corrigendum: 32 (1985), 159.
Bau-Sen Du, A Simple Method Which Generates Infinitely Many Congruence Identities, Fib. Quart. 27 (1989), 116-124.
Bau-Sen Du, A Simple Method Which Generates Infinitely Many Congruence Identities, arXiv:0706.2421 [math.NT], 2007.
Bau-Sen Du, The Minimal Number of Periodic Orbits of Periods Guaranteed in Sharkovskii's Theorem, arXiv:0706.2297 [math.DS], 2007.
MATHEMATICA
max = 100; Clear[b1, b2];
For[n = 1, n <= max, n++,
For[j = 1, j <= n, j++, b1[1][j, n] = 0; b1[2][j, n] = 1; b2[1][j, n] = b2[2][j, n] = 0];
b2[1][n, n] = b2[2][n, n] = 1];
For[k = 3, k <= max, k++,
For[n = 1, n <= max, n++,
For[j = 1, j <= n-1, j++, b1[k][j, n] = b1[k-2][1, n] + b1[k-2][j+1, n]; b2[k][j, n] = b2[k-2][1, n] + b2[k-2][j+1, n]];
b1[k][n, n] = b1[k-2][1, n] + b1[k-1][n, n]; b2[k][n, n] = b2[k-2][1, n] + b2[k-1][n, n]
]];
phin[n_] := Table[b2[m][n, n] + 2 Sum[If[m + 2 - 2 j > 0, b1[m + 2 - 2j][j, n], 0], {j, 1, n}], {m, 1, max}];
MT[s_List] := Table[DivisorSum[n, MoebiusMu[#] s[[n/#]]&]/n, {n, 1, Length[s]}];
MT[phin[4]] (* Jean-François Alcover, Nov 05 2018, adapted from Max Alekseyev's PARI script *)
PROG
(PARI) \\ implementation of MT() and phin() is given in A006207
MT(phin(4)) \\ sequence A_{n, 4} \\ Max Alekseyev, Feb 23 2012
CROSSREFS
KEYWORD
nonn
AUTHOR
EXTENSIONS
Terms a(32) onward from Max Alekseyev, Feb 23 2012
STATUS
approved