A006208 Generalized Fibonacci numbers A_{n,3}. (Formerly M0148)

1, 1, 0, 1, 0, 2, 1, 3, 2, 6, 4, 9, 8, 18, 16, 32, 32, 61, 64, 115, 128, 224, 258, 431, 520, 850, 1050, 1673, 2128, 3328, 4320, 6649, 8788, 13366, 17920, 26957, 36610, 54634, 74932, 111057, 153656, 226514, 315616, 463243, 649334, 949823, 1337984, 1951760

Offset

1,6

Comments

Bau-Sen Du's [1985/2007] Table 1, p. 6, has this sequence as the 4th column. - Jonathan Vos Post, Jun 18 2007

References

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Table of n, a(n) for n=1..48.

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.

Mathematica

max = 50;
Do[Do[b1[1][j, n] = 0; b1[2][j, n] = 1; b2[1][j, n] = b2[2][j, n] = 0, {j, n}]; b2[1][n, n] = b2[2][n, n] = 1, {n, max}];
Do[Do[Do[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], {j, n-1}]; 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], {n, max}], {k, 3, max}];
phin[n_] := Table[b2[m][n, n] + 2 Sum[If[m+2-2j > 0, b1[m+2-2j][j, n], 0], {j, n}], {m, max}];
MT[s_] := Table[DivisorSum[n, MoebiusMu[#] s[[n/#]]&]/n, {n, Length[s]}];
MT[phin[3]] (* Jean-François Alcover, Oct 01 2018, after Max Alekseyev in A006207 *)

Prog

(PARI) \\ implementation of MT() and phin() is given in A006207
MT(phin(3)) \\ sequence A_{n, 3} \\ Max Alekseyev, Feb 23 2012

Crossrefs

Cf. A006206 (A_{n,1}), A006207 (A_{n,2}), A006209 (A_{n,4}), A130628 (A_{n,5}), A208092 (A_{n,6}), A006210 (D_{n,2}), A006211 (D_{n,3}), A094392.

Sequence in context: A165045 A337452 A164768 * A026805 A335688 A206494

Adjacent sequences: A006205 A006206 A006207 * A006209 A006210 A006211

Keyword

nonn

Author

N. J. A. Sloane

Extensions

arxiv URL replaced with non-cached version, and duplicate of a reference removed, by R. J. Mathar, Oct 30 2009

Terms a(32) onward from Max Alekseyev, Feb 23 2012

Status

approved