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

Author

Paul Richards, Sep 21 2007

Keywords

• nonn

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.

Examples

			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...
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..10000
• Rémy Sigrist, C program for A133139

Crossrefs

Cf. A002858.

Programs

C

See Links section.

Extensions

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