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

Author

M. F. Hasler, Feb 10 2008

Keywords

• nonn
• easy

Comments

See A137743 for comments and examples.

Links

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

Crossrefs

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

Programs

Mathematica

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

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])

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

Extensions

More terms from Colin Barker, Nov 04 2013