This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A103373 a(1) = a(2) = a(3) = a(4) = a(5) = a(6) = 1 and for n>6: a(n) = a(n-5) + a(n-6). 17
 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 4, 4, 4, 4, 5, 7, 8, 8, 8, 9, 12, 15, 16, 16, 17, 21, 27, 31, 32, 33, 38, 48, 58, 63, 65, 71, 86, 106, 121, 128, 136, 157, 192, 227, 249, 264, 293, 349, 419, 476, 513, 557, 642, 768, 895, 989, 1070, 1199, 1410, 1663, 1884, 2059, 2269 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,7 COMMENTS k=5 case of the family of sequences whose k=1 case is the Fibonacci sequence A000045, k=2 case is the Padovan sequence A000931 (offset so as to begin 1,1,1), k=3 case is A079398 (offset so as to begin 1,1,1,1) and k=4 case is A103372. The general case for integer k>1 is defined: a(1) = a(2) = ... = a(k+1) and for n>(k+1) a(n) = a(n-k) + a(n-[k+1]). For this k=5 case, the ratio of successive terms a(n)/a(n-1) approaches the unique positive root of the characteristic polynomial: x^6 - x - 1 = 0. This is the real constant (to 100 digits accuracy): 1.134724138401519492605446054506472840279667226382801485925149551668236893999842671279689011614820249 The sequence of prime values in this k=5 case is A103383; The sequence of semiprime values in this k=5 case is A103393. REFERENCES Selmer, E.S., "On the irreducibility of certain trinomials", Math. Scand., 4 (1956) 287-302 Shallit, J., "A generalization of automatic sequences", Theoretical Computer Science, 61(1988)1-16. Zanten, A. J. van, "The golden ratio in the arts of painting, building and mathematics", Nieuw Archief voor Wiskunde, 4 (17) (1999) 229-245. LINKS Richard Padovan, Dom Hans van der Laan and the Plastic Number. J.-P. Allouche and T. Johnson, Narayana's Cows and Delayed Morphisms Index to sequences with linear recurrences with constant coefficients, signature (0,0,0,0,1,1). FORMULA G.f. -x*(1+x+x^2+x^3+x^4) / ( -1+x^5+x^6 ). - R. J. Mathar, Aug 26 2011 EXAMPLE a(22) = 9 because a(22) = a(22-5) + a(22-6) = a(17) + a(16) = 5 + 4 = 9. MATHEMATICA k = 5; Do[a[n] = 1, {n, k + 1}]; a[n_] := a[n] = a[n - k] + a[n - k - 1]; Array[a, 65] CROSSREFS Cf. A000045, A000931, A079398, A103372-A103381, A103383, A103393. Sequence in context: A025780 A199121 A109697 * A038539 A109368 A046774 Adjacent sequences:  A103370 A103371 A103372 * A103374 A103375 A103376 KEYWORD nonn,easy AUTHOR Jonathan Vos Post, Feb 03 2005 EXTENSIONS Edited by Ray Chandler and Robert G. Wilson v, Feb 06 2005 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Transforms | Puzzles | Hot | Classics
Recent Additions | More pages | Superseeker | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement .