cp's OEIS Frontend

A214835 Total sum of lengths of formula representations of n using addition, multiplication and the constant 1.

%I A214835 #18 Jul 19 2017 16:03:41
%S A214835 1,3,10,42,144,564,2064,7944,30252,117000,453192,1768480,6917504,
%T A214835 27163232,106923648,421931308,1668250408,6608054656,26215991648,
%U A214835 104154492224,414324786144,1650080158832,6578448714144,26251704924528,104850927048448,419119282453408
%N A214835 Total sum of lengths of formula representations of n using addition, multiplication and the constant 1.
%H A214835 Alois P. Heinz, <a href="/A214835/b214835.txt">Table of n, a(n) for n = 1..100</a>
%H A214835 Edinah K. Ghang, Doron Zeilberger, <a href="https://arxiv.org/abs/1303.0885v1">Zeroless Arithmetic: Representing Integers ONLY using ONE</a>, arXiv:1303.0885v1 [math.CO], 2013
%H A214835 Shalosh B. Ekhad, <a href="http://www.math.rutgers.edu/~zeilberg/tokhniot/oArithFormulas1">Everything About Formulas Representing Integers Using Additions and Multiplication for integers from 1 to 8000</a>
%H A214835 Wikipedia, <a href="https://en.wikipedia.org/wiki/Postfix_notation">Postfix notation</a>
%H A214835 <a href="/index/Com#complexity">Index to sequences related to the complexity of n</a>
%e A214835 a(1) = 1: 1.
%e A214835 a(2) = 3: 11+.
%e A214835 a(3) = 10: 111++, 11+1+.
%e A214835 a(4) = 42: 1111+++, 111+1++, 11+11++, 111++1+, 11+1+1+, 11+11+*.
%e A214835 a(5) = 144: 11111++++, 1111+1+++, 111+11+++, 1111++1++, 111+1+1++, 111+11+*+, 11+111+++, 11+11+1++, 111++11++, 11+1+11++, 1111+++1+, 111+1++1+, 11+11++1+, 111++1+1+, 11+1+1+1+, 11+11+*1+.
%Y A214835 Cf. A005245, A214833 (number of formula representations), A213923 (minimal length of formula), A005408(n-1) (maximal length of formula).
%K A214835 nonn
%O A214835 1,2
%A A214835 _Alois P. Heinz_, Mar 07 2013