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A054552
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4n^2 - 3n + 1.
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21
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1, 2, 11, 28, 53, 86, 127, 176, 233, 298, 371, 452, 541, 638, 743, 856, 977, 1106, 1243, 1388, 1541, 1702, 1871, 2048, 2233, 2426, 2627, 2836, 3053, 3278, 3511, 3752, 4001, 4258, 4523, 4796, 5077, 5366, 5663, 5968, 6281, 6602, 6931, 7268, 7613, 7966, 8327
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Also indices in any spiral organized like A054551.
Equals binomial transform of [1, 1, 8, 0, 0, 0,...]. - Gary W. Adamson (qntmpkt(AT)yahoo.com), May 11 2008
Ulam's spiral (E spoke). - Robert G. Wilson v, Oct 31 2011
For n > 0: left edge of the triangle A033293. [Reinhard Zumkeller, Jan 18 2012]
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LINKS
| Harvey P. Dale, Table of n, a(n) for n = 0..1000
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FORMULA
| G.f.: (1-x+8*x^2)/(1-x)^3.
a(n)=8*n+a(n-1)-7 (with a(0)=1) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Aug 07 2010]
a(0)=1, a(1)=2, a(2)=11, a(n)=3*a(n-1)-3*a(n-2)+a(n-3) [From Harvey P. Dale, Oct 10 2011]
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EXAMPLE
| 10 11...: a(2)=11
.9 .2 .3: a(1)= 2
.8 .1 .4: a(0)= 1
.7 .6 .5
a(1)=8*1+1-7=2; a(2)=8*2+2-7=11; a(3)=8*3+11-7=28 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Aug 07 2010]
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MATHEMATICA
| f[n_] := 4*n^2 - 3*n + 1; Array[f, 50] [From Vladimir Orlovsky, Sep 01 2008]
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PROG
| (PARI) a(n)= 4*n^2-3*n+1 \\ Charles R Greathouse IV, Jan 15 2012
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CROSSREFS
| Cf. A054551, A108781.
Sequence in context: A139211 A161527 A143651 * A034534 A045493 A116038
Adjacent sequences: A054549 A054550 A054551 * A054553 A054554 A054555
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KEYWORD
| easy,nonn
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AUTHOR
| Enoch Haga and G. L. Honaker, Jr. (Enokh(AT)comcast.net), Apr 09 2000
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