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.
%I A339371 #5 Dec 02 2020 09:00:25
%S A339371 1,0,1,1,3,2,5,4,8,7,13,12,18,18,27,27,39,38,53,53,72,73,96,98,126,
%T A339371 128,165,168,209,216,266,274,334,345,416,430,514,533,628,655,766,797,
%U A339371 929,966,1115,1164,1336,1395,1590,1661,1885,1969,2226,2326,2611,2734
%N A339371 Number of partitions of n into an even number of Fibonacci parts (with a single type of 1).
%H A339371 <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F A339371 G.f.: (1/2) * (Product_{k>=2} 1 / (1 - x^Fibonacci(k)) + Product_{k>=2} 1 / (1 + x^Fibonacci(k))).
%F A339371 a(n) = (A003107(n) + A298949(n)) / 2.
%e A339371 a(7) = 4 because we have [5, 2], [3, 2, 1, 1], [2, 2, 2, 1] and [2, 1, 1, 1, 1, 1].
%t A339371 nmax = 55; CoefficientList[Series[(1/2) (Product[1/(1 - x^Fibonacci[k]), {k, 2, 26}] + Product[1/(1 + x^Fibonacci[k]), {k, 2, 26}]), {x, 0, nmax}], x]
%Y A339371 Cf. A000045, A003107, A027187, A093997, A093998, A298949, A339372.
%K A339371 nonn
%O A339371 0,5
%A A339371 _Ilya Gutkovskiy_, Dec 02 2020