cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A241951 Number of possible representations of n as a sum of distinct positive integers from the Fibonacci and Lucas sequences 0,1,1,2,3,5,8,13,... and 2,1,3,4,7,11,... (A000045 and A000032).

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%I A241951 #11 Jan 05 2025 19:51:40
%S A241951 1,1,1,2,2,3,3,4,5,5,6,7,8,9,10,11,12,12,15,15,16,19,19,21,22,24,26,
%T A241951 26,28,31,31,33,35,37,40,40,44,45,46,51,51,54,57,58,61,62,65,70,69,72,
%U A241951 76,76,81,81,86,90,89,95,97,100,105,105,110,114,114,121,121,126,133,131,138,139,142,149,147,154,160,159,165,167
%N A241951 Number of possible representations of n as a sum of distinct positive integers from the Fibonacci and Lucas sequences 0,1,1,2,3,5,8,13,... and 2,1,3,4,7,11,... (A000045 and A000032).
%H A241951 Alois P. Heinz, <a href="/A241951/b241951.txt">Table of n, a(n) for n = 0..20000</a>
%H A241951 D. A. Klarner, Representations of N as a sum of distinct elements from special sequences, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Scanned/4-4/klarner-a.pdf">part 1</a>, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Scanned/4-4/klarner-b.pdf">part 2</a>, Fib. Quart., 4 (1966), 289-306 and 322.
%e A241951 a(10) = 6 because 10 can be represented in 6 possible ways as a sum of integers in the set {1,2,3,4,5,7,8,11,13,...}: 8+2, 7+3, 7+2+1, 5+4+1, 5+3+2, 4+3+2+1.
%Y A241951 Cf. A000045, A000032, A000119.
%K A241951 nonn
%O A241951 0,4
%A A241951 _Casey Mongoven_, May 03 2014
%E A241951 a(0)=1 from _Alois P. Heinz_, Sep 16 2015