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 A102379 #22 May 02 2025 03:51:12 %S A102379 0,1,2,4,6,9,12,17,22,29,36,46,56,69,82,100,118,141,164,194,224,261, %T A102379 298,345,392,449,506,576,646,729,812,913,1014,1133,1252,1394,1536, %U A102379 1701,1866,2061,2256,2481,2706,2968,3230,3529,3828,4174,4520,4913 %N A102379 a(n) is the minimal number of nodes in a binary tree of height n. %C A102379 Conjecture: Let b(n) be the number of fixed points of the set of binary partitions of n under Glaisher's function that proves Euler's odd-distinct theorem. Then b(1) = 1 and for n > 1, b(2*n) = b(2*n+1) = 2*a(n). - _George Beck_, Jul 23 2022 %D A102379 de Bruijn, N. G., On Mahler's partition problem. Nederl. Akad. Wetensch., Proc. 51, (1948) 659-669 = Indagationes Math. 10, 210-220 (1948). %D A102379 Gonnet, Gaston H.; Olivie, Henk J.; and Wood, Derick, Height-ratio-balanced trees. Comput. J. 26 (1983), no. 2, 106-108. %D A102379 Mahler, Kurt On a special functional equation. J. London Math. Soc. 15, (1940). 115-123. %D A102379 Nievergelt, J.; Reingold, E. M., Binary search trees of bounded balance, SIAM J. Comput. 2 (1973), 33-43. %F A102379 a(n) = a(n-1) + a(floor(n/2)) + 1, a(1) = 0. %F A102379 a(n) - a(n-1) = A018819(n+1). %F A102379 G.f. A(x) satisfies (1-x)*A(x) = 2*(1 + x)*B(x^2), where B(x) is the g.f. of A033485. %o A102379 (Python) %o A102379 from functools import cache %o A102379 @cache %o A102379 def a(n: int) -> int: %o A102379 return a(n - 1) + a(n // 2) + 1 if n > 1 else 0 %o A102379 print([a(n) for n in range(1, 51)]) # _Peter Luschny_, Jul 24 2022 %Y A102379 Cf. A000123, A033485, A102378. %Y A102379 Essentially partial sums of A040039. %K A102379 nonn %O A102379 1,3 %A A102379 _Mitch Harris_, Jan 05 2005