A137739 Number of different strings of length n+6 obtained from "123...n" by iteratively duplicating any substring.

1, 64, 355, 1014, 2218, 4217, 7343, 12018, 18767, 28233, 41193, 58575, 81476, 111181, 149183, 197204, 257217, 331469, 422505, 533193, 666750, 826769, 1017247, 1242614, 1507763, 1818081, 2179481, 2598435, 3082008, 3637893, 4274447, 5000728, 5826533, 6762437

Offset: 1

Author

M. F. Hasler, Feb 10 2008

Keywords

• nonn
• easy

Comments

See A137743 for comments and examples.

Links

• Index entries for doubling substrings
• Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

Crossrefs

Cf. A137740-A137743, A135473, A137744-A137748.

Programs

PARI

A137739(n)=if(n<2,1,n=A135473(n+6,n);n[ #n]) /* function A135473 defined in A137743 */

PARI

A137739(n)=if(n>4,n*(n*(n*(n*(n*(n+45)+775)+5775)[phone])/6!-112,[1,64,355,1014][n])

Formula

a(n) = 1/720*(n+9)*(n^5+36*n^4+451*n^3+1716*n^2-380*n-8880)-1 for n>4.

G.f.: x*(x^10+3*x^9-6*x^8-26*x^7+221*x^5-370*x^4+162*x^3+72*x^2-57*x-1) / (x-1)^7. - Colin Barker, Nov 04 2013

Extensions

More terms from Colin Barker, Nov 04 2013