A137741 Number of different strings of length n+4 obtained from "123...n" by iteratively duplicating any substring.

1, 16, 54, 119, 218, 360, 555, 814, 1149, 1573, 2100, 2745, 3524, 4454, 5553, 6840, 8335, 10059, 12034, 14283, 16830, 19700, 22919, 26514, 30513, 34945, 39840, 45229, 51144, 57618, 64685, 72380, 80739, 89799, 99598, 110175, 121570, 133824, 146979, 161078

Offset

1,2

Comments

See A137743 for comments and examples.

Links

Table of n, a(n) for n=1..40.

Index entries for doubling substrings

Formula

a(n) = n^4 for n=1,2; a(n) = 1/24*(n+3)*(n^3+15*n^2+50*n-96) for n>2 (conjectured).

G.f.: x*(x^6+x^5-8*x^4+x^3+16*x^2-11*x-1) / (x-1)^5 (conjectured). - Colin Barker, Nov 04 2013

Prog

(PARI) A137741(n)=if(n<2, 1, n=A135473(n+4, n); n[ #n]) /* function A135473 defined in A137743 */

Crossrefs

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

Sequence in context: A334643 A197246 A187104 * A167690 A297842 A172190

Adjacent sequences: A137738 A137739 A137740 * A137742 A137743 A137744

Keyword

nonn,easy

Author

M. F. Hasler, Feb 10 2008

Extensions

More terms from Colin Barker, Nov 04 2013

Status

approved