A137740 Number of different strings of length n+5 obtained from "123...n" by iteratively duplicating any substring.

1, 32, 138, 348, 700, 1246, 2050, 3188, 4749, 6836, 9567, 13076, 17514, 23050, 29872, 38188, 48227, 60240, 74501, 91308, 110984, 133878, 160366, 190852, 225769, 265580, 310779, 361892, 419478, 484130, 556476, 637180, 726943, 826504, 936641, 1058172, 1191956

Offset

1,2

Comments

See A137743 for comments and examples.

Links

Table of n, a(n) for n=1..37.

Index entries for doubling substrings

Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).

Formula

a(n) = (n+4)(n^2+3n-8)(n^2+23n+150)/5!+4 for n>4.

G.f.: x*(x^8+2*x^7-7*x^6-20*x^5+57*x^4-20*x^3-39*x^2+26*x+1) / (x-1)^6. - Colin Barker, Nov 04 2013

Mathematica

LinearRecurrence[{6, -15, 20, -15, 6, -1}, {1, 32, 138, 348, 700, 1246, 2050, 3188, 4749}, 40] (* Harvey P. Dale, Oct 18 2020 *)

Prog

(PARI) A137740(n)=if(n<2, 1, n=A135473(n+5, n); n[ #n]) /* function A135473 defined in A137743 */
(PARI) A137740(n)=if(n>4, n*(n*(n*(n*(n+30)+315)+1110)-136)/5!-36, [1, 32, 138, 348][n])

Crossrefs

Cf. A137739-A137743, A135473, A137744-A137748.

Sequence in context: A299386 A299185 A299946 * A221597 A159763 A100164

Adjacent sequences: A137737 A137738 A137739 * A137741 A137742 A137743

Keyword

nonn,easy

Author

M. F. Hasler, Feb 10 2008

Extensions

More terms from Colin Barker, Nov 04 2013

Status

approved