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1, 4, 11, 22, 37, 56, 79, 106, 137, 172, 211, 254, 301, 352, 407, 466, 529, 596, 667, 742, 821, 904, 991, 1082, 1177, 1276, 1379, 1486, 1597, 1712, 1831, 1954, 2081, 2212, 2347, 2486, 2629, 2776, 2927, 3082, 3241, 3404, 3571, 3742, 3917, 4096, 4279, 4466
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| a(n)=A058331(n)+A000027(n).
a(n) = A014105(n) + 1; A100035(a(n)) = 1. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Oct 31 2004
Equals (1, 2, 3,...) convolved with (1, 2, 4, 4, 4,...). a(3) = 22 = (1, 2, 3, 4) dot (4, 4, 2, 1) = (4 + 8 + 6 + 4). [From Gary W. Adamson (qntmpkt(AT)yahoo.com), May 01 2009]
a(n) is also the number of ways to place 2 nonattacking bishops on a 2 X (n+1) board. [From Vaclav Kotesovec (kotesovec(AT)chello.cz), Jan 29 2010]
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REFERENCES
| Aoife Hennessy, A Study of Riordan Arrays with Applications to Continued Fractions, Orthogonal Polynomials and Lattice Paths, Ph. D. Thesis, Waterford Institute of Technology, Oct. 2011; http://repository.wit.ie/1693/1/AoifeThesis.pdf
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LINKS
| Guo-Niu Han, Enumeration of Standard Puzzles
Index entries for sequences related to linear recurrences with constant coefficients, signature (3,-3,1).
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FORMULA
| G.f.: (1+x+2x^2)/(1 - x)^3.
a(n)=ceiling((2n+1)^2/2)-n=A001844(n)-n; - Paul Barry (pbarry(AT)wit.ie), Jul 16 2006
Row sums of triangle A131901. A084849 = binomial transform of (1, 3, 4, 0, 0, 0,...). - Gary W. Adamson (qntmpkt(AT)yahoo.com), Jul 26 2007
Equals A134082 * [1,2,3,...]. - Gary W. Adamson (qntmpkt(AT)yahoo.com), Oct 07 2007
a(n)=(1+A000217(2n-1)+A000217(2n+1))/2 [From Enrique Perez Herrero (psychgeometry(AT)gmail.com), Apr 02 2010]
a(n)=(A177342(n+1)-A177342(n))/2, with n>0. [From Bruno Berselli (berselli.bruno(AT)yahoo.it), May 19 2010]
a(n)-3*a(n-1)+3*a(n-2)-a(n-3)=0, with n>2. [From Bruno Berselli (berselli.bruno(AT)yahoo.it), May 24 2010]
a(n)=4*n+a(n-1)-1 (with a(0)=1) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Aug 08 2010]
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EXAMPLE
| For n=5, a(5)=(A177342(6)-A177342(5))/2=(261-149)/2=56. [From Bruno Berselli (berselli.bruno(AT)yahoo.it), May 19 2010]
a(1)=4*1+1-1=4; a(2)=4*2+4-1=11; a(3)=4*3+11-1=22; a(4)=4*4+22-1=37 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Aug 08 2010]
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MATHEMATICA
| s = 1; lst = {s}; Do[s += n + 2; AppendTo[lst, s], {n, 1, 200, 4}]; lst [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 11 2009]
f[n_]:=(n*(2*n+1)+1); Table[f[n], {n, 5!}] [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Feb 07 2010]
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CROSSREFS
| Cf. A100040, A100041, A100036, A100037, A100038, A100039, A131901, A134082.
Cf. A004767 (first differences).
Sequence in context: A038414 A008154 A008162 * A008265 A160424 A008229
Adjacent sequences: A084846 A084847 A084848 * A084850 A084851 A084852
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KEYWORD
| easy,nonn,changed
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Jun 09 2003
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