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A137742
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a(n) = (n-1)*(n+4)*(n+6)/6 for n>1, a(1)=1.
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5
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1, 8, 21, 40, 66, 100, 143, 196, 260, 336, 425, 528, 646, 780, 931, 1100, 1288, 1496, 1725, 1976, 2250, 2548, 2871, 3220, 3596, 4000, 4433, 4896, 5390, 5916, 6475, 7068, 7696, 8360, 9061, 9800, 10578, 11396, 12255, 13156, 14100, 15088, 16121, 17200, 18326, 19500
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Also the number of different strings of length n+3 obtained from "123...n" by iteratively duplicating any substring (see A137743 for comments and examples). This is the principal (although not simplest) definition of this sequence and explains why a(1)=1 and not 0.
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 0..10000
Index entries for doubling substrings
Index to sequences with linear recurrences with constant coefficients, signature (4,-6,4,-1).
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FORMULA
| Contribution by Bruno Berselli, Aug 23 2011: (Start)
G.f.: x*(1+4*x-5*x^2+x^4)/(1-x)^4.
a(n) = +4*a(n-1) -6*a(n-2) +4*a(n-3) -a(n-4).
a(-n-7) = -A000297(n). (End)
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MATHEMATICA
| Join[{1}, Table[Binomial[n, 3]-2*n, {n, 6, 60}]] (*or*) Join[{1}, Table[(n-1)(n+4)(n+6)/6, {n, 2, 56}]] (* From Vladimir Joseph Stephan Orlovsky, Apr 22 2011 *)
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PROG
| (PARI) A137742(n)=if(n<2, 1, n=A135473(n+3, n); n[ #n]) /* function A135473 defined in A137743 */
(PARI) A137742(n)=if(n<2, 1, (n - 1)*(n + 4)*(n + 6)/6)
(MAGMA) [1] cat [(n^3+9*n^2+14*n-24)/6: n in [2..46]]; // Bruno Berselli, Aug 23 2011
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CROSSREFS
| Cf. A137740-A137743, A135473, A137744-A137748.
Sequence in context: A179681 A000567 A124484 * A190456 A188026 A180672
Adjacent sequences: A137739 A137740 A137741 * A137743 A137744 A137745
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KEYWORD
| nonn,easy
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AUTHOR
| M. F. Hasler (www.univ-ag.fr/~mhasler), Feb 10 2008
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