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

1,2

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

Example

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+.

Crossrefs

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

Sequence in context: A009364 A308951 A295236 * A149059 A129878 A094558

Adjacent sequences: A214832 A214833 A214834 * A214836 A214837 A214838

Keyword

nonn

Author

Alois P. Heinz, Mar 07 2013

Status

approved