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A137739 Number of different strings of length n+6 obtained from "123...n" by iteratively duplicating any substring. 4
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified April 13 13:24 EDT 2021. Contains 342936 sequences. (Running on oeis4.)