A006209 Generalized Fibonacci numbers A_{n,4}.
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
Offset: 1
Keywords
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.
Crossrefs
Programs
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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 *) -
PARI
\\ implementation of MT() and phin() is given in A006207 MT(phin(4)) \\ sequence A_{n,4} \\ Max Alekseyev, Feb 23 2012
Extensions
Terms a(32) onward from Max Alekseyev, Feb 23 2012