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A214835 Total sum of lengths of formula representations of n using addition, multiplication and the constant 1. 2
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified July 28 15:08 EDT 2021. Contains 346335 sequences. (Running on oeis4.)