A292225 Row sums of irregular triangle A292224. a(n) gives the total number of admissible tuples starting with 0 in the interval [0, 1, ..., n-1].

1, 1, 2, 2, 3, 3, 6, 6, 10, 10, 14, 14, 28, 28, 41, 41, 57, 57, 105, 105, 160, 160, 210, 210, 383, 383, 531, 531, 678, 678, 1343, 1343, 1923, 1923, 2482, 2482, 4402, 4402, 5849, 5849, 7824, 7824, 14064, 14064, 18292, 18292, 23981, 23981, 39745, 39745, 57307, 57307, 71639, 71639, 117846, 117846

Offset: 1

Author

Wolfdieter Lang, Oct 09 2017

Keywords

• nonn

Comments

This sequence is given in column 2 of Table 2, p. 27, of the Engelsma link.

See A292224 for the reason for the repetitions for n = 2*k+1 and n = 2*(k+1) for k >= 0, the definition of "admissible", references, and examples of these admissible k-tuples for n = 1..10 (with k = 1, 2, ..., A023193(n)).

Links

• Thomas J. Engelsma, Permissible Patterns of Primes, September 2009, Table 2, p. 27.

Crossrefs

Cf. A023189, A023193, A292224.

Formula

a(n) = Sum_{k=1..A023193(n)} A292224(n, k), for n >= 1.

a(2*n+1) = a(2*n) + A023189(n+1). - Pontus von Brömssen, Aug 21 2025

Extensions

Terms a(27) .. a(56) from Engelsma's Table 2 (there are also a(57)..a(62) given but a(62) should be 364545 if a(61) = 364545 is correct). - Wolfdieter Lang, Oct 17 2017