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

1, 3, 10, 42, 144, 564, 2064, 7944, 30252, 117000, 453192, 1768480, 6917504, 27163232, 106923648, 421931308, 1668250408, 6608054656, 26215991648, 104154492224, 414324786144, 1650080158832, 6578448714144, 26251704924528, 104850927048448, 419119282453408

Offset: 1

Author

Alois P. Heinz, Mar 07 2013

Keywords

• nonn

Examples

			a(1) = 1: 1.
a(2) = 3: 11+.
a(3) = 10: 111++, 11+1+.
a(4) = 42: 1111+++, 111+1++, 11+11++, 111++1+, 11+1+1+, 11+11+*.
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+.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..100
• Edinah K. Ghang, Doron Zeilberger, Zeroless Arithmetic: Representing Integers ONLY using ONE, arXiv:1303.0885v1 [math.CO], 2013
• Shalosh B. Ekhad, Everything About Formulas Representing Integers Using Additions and Multiplication for integers from 1 to 8000
• Wikipedia, Postfix notation
• Index to sequences related to the complexity of n

Crossrefs

Cf. A005245, A214833 (number of formula representations), A213923 (minimal length of formula), A005408(n-1) (maximal length of formula).