A133139 Number of generalized Ulam sequences including n as the third or higher term.

0, 0, 1, 2, 3, 5, 6, 10, 9, 12, 14, 17, 20, 20, 20, 29, 28, 31, 35, 35, 37, 40, 45, 51, 49, 55, 55, 58, 64, 61, 71, 76, 74, 76, 78, 87, 92, 91, 99, 97, 107, 100, 114, 107, 112, 119, 128, 132, 133, 127, 142, 140, 151, 146, 151, 154, 170, 158, 172, 164, 185, 179, 184, 186

Offset

1,4

Comments

I generalize the Ulam sequence by allowing any positive integer values (i and j) for the first two terms. Subsequent terms are all those integers which are a unique sum of two distinct earlier terms. In this sequence, a(n) is the number of distinct sequences (as defined by the first two terms) where 1 <= i < n-1 and i < j <= n-1.

Links

Rémy Sigrist, Table of n, a(n) for n = 1..10000

Rémy Sigrist, C program for A133139

Example

a(10) = 12, since 10 occurs as a term in 12 different generalized Ulam sequences. The first two values of each are: (1,3) (1,4) (1,5) (1,6) (1,7) (1,8) (1,9) (2,6) (2,8) (3,4) (3,7) (4,6). It does not occur in the sequence (1,2) which runs: 1, 2, 3, 4, 6, 8, 11...

Prog

(C) See Links section.

Crossrefs

Cf. A002858.

Sequence in context: A051896 A061939 A029503 * A162309 A014593 A261088

Adjacent sequences: A133136 A133137 A133138 * A133140 A133141 A133142

Keyword

nonn

Author

Paul Richards, Sep 21 2007

Extensions

Spelling/notation corrections by Charles R Greathouse IV, Mar 18 2010

Status

approved