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1, 10, 19, 28, 37, 46, 55, 64, 73, 82, 91, 100, 109, 118, 127, 136, 145, 154, 163, 172, 181, 190, 199, 208, 217, 226, 235, 244, 253, 262, 271, 280, 289, 298, 307, 316, 325, 334, 343, 352, 361, 370, 379, 388, 397, 406, 415, 424, 433, 442, 451, 460, 469, 478
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Also all the numbers with digital root 1; A010888(a(n)) = 1. [From Rick L. Shepherd (rshepherd2(AT)hotmail.com), Jan 12 2009]
A116371(a(n))=A156144(a(n)); positions where records occur in A156144: A156145(n+1)=A156144(a(n)). [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Feb 05 2009]
If A=[A147296] 9*n^2+2*n (n>0, 11, 40, 87,.); Y=[A010701] 3 (3, 3, 3,.,); X=[A017173] 9*n+1 (n>0, 10, 19, 28.,), we have, for all terms, Pell's equation X^2-A*Y^2=1. Example: 10^2-11*3^2=1; 19^2-40*3^2=1; 28^2-87*3^2=1. [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Aug 01 2010]
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LINKS
| Tanya Khovanova, Recursive Sequences
Index to sequences with linear recurrences with constant coefficients, signature (2,-1).
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FORMULA
| G.f.: (1+8*x)/(1-x)^2.
a(n)=2*a(n-1)-a(n-2) with a(0)=1, a(1)=10 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Aug 01 2010]
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EXAMPLE
| For n=2, a(2)=2*10-1=19; n=3, a(3)=2*19-10=28; n=4, a(4)=2*28-19=37 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Aug 01 2010]
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MATHEMATICA
| Range[1, 1000, 9] (* From Vladimir Joseph Stephan Orlovsky (4vladimir(AT)gmail.com), May 28 2011 *)
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PROG
| (Other) sage: [i+1 for i in range(480) if gcd(i, 9) == 9] # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 20 2009]
(PARI) forstep(n=1, 500, 9, print1(n", ")) \\ Charles R Greathouse IV, May 28 2011
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CROSSREFS
| Cf. A093644 ((9, 1) Pascal, column m=1).
Cf. A010888. [From Rick L. Shepherd (rshepherd2(AT)hotmail.com), Jan 12 2009]
Cf. A147296, A010701 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Mar 11 2009]
Sequence in context: A098750 A089756 A097153 * A088410 A179110 A126624
Adjacent sequences: A017170 A017171 A017172 * A017174 A017175 A017176
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KEYWORD
| nonn,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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