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

1,2

Comments

See A137743 for comments and examples.

Links

Table of n, a(n) for n=1..34.

Index entries for doubling substrings

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

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

Prog

(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+45)+775)+5775)+15064)-12300)/7!-112, [1, 64, 355, 1014][n])

Crossrefs

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

Sequence in context: A299805 A299681 A300313 * A281468 A302622 A302414

Adjacent sequences: A137736 A137737 A137738 * A137740 A137741 A137742

Keyword

nonn,easy

Author

M. F. Hasler, Feb 10 2008

Extensions

More terms from Colin Barker, Nov 04 2013

Status

approved