The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A003520

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A003520

a(n) = a(n-1) + a(n-5); a(0) = ... = a(4) = 1.
(history; published version)

#183 by N. J. A. Sloane at Wed Sep 11 00:38:52 EDT 2024

STATUS

proposed

approved

#182 by Michael De Vlieger at Tue Sep 10 16:47:34 EDT 2024

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editing

proposed

#181 by Michael De Vlieger at Tue Sep 10 16:47:26 EDT 2024

LINKS

Michael A. Allen, <a href="https://arxiv.org/abs/2409.00624">Connections between Combinations Without Specified Separations and Strongly Restricted Permutations, Compositions, and Bit Strings</a>, arXiv:2409.00624 [math.CO], 2024. See pp. 18, 22.

STATUS

approved

editing

#180 by Joerg Arndt at Fri Aug 02 04:02:51 EDT 2024

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reviewed

approved

#179 by Michel Marcus at Fri Aug 02 04:00:37 EDT 2024

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proposed

reviewed

#178 by Jason Yuen at Fri Aug 02 03:21:56 EDT 2024

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editing

proposed

#177 by Jason Yuen at Fri Aug 02 03:21:53 EDT 2024

COMMENTS

This comment covers a family of sequences which satisfy a recurrence of the form a(n) = a(n-1) + a(n-m), with a(n) = 1 for n = 0..m-1. The generating function is 1/(1-x-x^m). Also a(n) = sum(Sum_{i=0..n/m} binomial(n-(m-1)*i, i), i=0..n/m). This family of binomial summations or recurrences gives the number of ways to cover (without overlapping) a linear lattice of n sites with molecules that are m sites wide. Special case: m=1: A000079; m=4: A003269; m=5: A003520; m=6: A005708; m=7: A005709; m=8: A005710.

STATUS

approved

editing

#176 by Harvey P. Dale at Wed Sep 27 16:11:50 EDT 2023

STATUS

editing

approved

#175 by Harvey P. Dale at Wed Sep 27 16:11:46 EDT 2023

MATHEMATICA

nxt[{a_, b_, c_, d_, e_}]:={b, c, d, e, e+a}; NestList[nxt, {1, 1, 1, 1, 1}, 50][[;; , 1]] (* Harvey P. Dale, Sep 27 2023 *)

STATUS

approved

editing

#174 by N. J. A. Sloane at Thu May 25 07:04:03 EDT 2023

STATUS

editing

approved