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A006209 Generalized Fibonacci numbers A_{n,4}.
(Formerly M0027)
7
1, 1, 0, 1, 0, 2, 0, 3, 1, 6, 2, 9, 4, 18, 8, 30, 16, 56, 32, 101, 64, 191, 128, 351, 256, 668, 512, 1257, 1026, 2402, 2056, 4592, 4122, 8854, 8272, 17092, 16608, 33212, 33364, 64674, 67072, 126490, 134912, 248038, 271528, 487986, 546818, 962350 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,6

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.

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-Fran├žois 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

Cf. A006206 (A_{n,1}), A006207 (A_{n,2}), A006208 (A_{n,3}), A130628 (A_{n,5}), A208092 (A_{n,6}), A006210 (D_{n,2}), A006211 (D_{n,3}), A094392.

Sequence in context: A166117 A078051 A130627 * A005307 A143351 A241644

Adjacent sequences:  A006206 A006207 A006208 * A006210 A006211 A006212

KEYWORD

nonn

AUTHOR

N. J. A. Sloane

EXTENSIONS

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

STATUS

approved

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Last modified November 14 22:17 EST 2019. Contains 329134 sequences. (Running on oeis4.)