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A137741 Number of different strings of length n+4 obtained from "123...n" by iteratively duplicating any substring. 4
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 (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..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: A164324 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

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Last modified November 20 20:54 EST 2018. Contains 317422 sequences. (Running on oeis4.)