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Search: id:A095794
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| 1, 6, 14, 25, 39, 56, 76, 99, 125, 154, 186, 221, 259, 300, 344, 391, 441, 494, 550, 609, 671, 736, 804, 875, 949, 1026, 1106, 1189, 1275, 1364, 1456, 1551, 1649, 1750, 1854, 1961, 2071, 2184, 2300, 2419, 2541, 2666, 2794, 2925, 3059, 3196, 3336, 3479, 3625
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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a(n) = A126890(n+1,n-2) for n>1. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Dec 30 2006
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FORMULA
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a(n) = (3/2)n^2 + (1/2)n - 1. a(n+3), (n>3) = 3*a(n+2) - 3*a(n+1) + a(n). a(n+1) right term in M^n * [1 1 1].
sum (n+j-1,j=0..n). - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Sep 12 2006
Row sums of triangle A131414.
Equals binomial transform of (1, 5, 3, 0, 0, 0,...). Equals A051340 * (1, 2, 3,...).
G.f.: x*(-1-3*x+x^2)/(-1+x)^3 = 1-3/(-1+x)^3-4/(-1+x)^2 . - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 19 2007
a(n)=3*n+a(n-1)-1 (with a(1)=1) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Nov 08 2009]
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EXAMPLE
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1. a(4) = 25 = A005449(4) - 1
2. a(5) = 39 = f(n), n=5 in (3/2)n^2 + (1/2)n - 1.
3. a(7) = 76 = 3*56 - 3*39 + 25
4. a(5) = 39 = right term of M^4 * [1 1 1] = [1 5 39].
For n=2, a(2)=3*2+1-1=6; n=3, a(3)=3*3+6-1=14: n=4, a(4)=3*4+14-1=25 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Nov 08 2009]
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MAPLE
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A005449 := proc(n) RETURN(n*(3*n+1)/2) ; end: A095794 := proc(n) RETURN(A005449(n)-1) ; end: for n from 1 to 100 do printf("%a, ", A095794(n)) ; od: - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jun 23 2006
a[0]:=0:a[1]:=1:for n from 2 to 50 do a[n]:=2*a[n-1]-a[n-2]-3 od: seq(-a[n], n=2..50); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Feb 18 2008
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MATHEMATICA
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a[n_]:=Sum[i+n-3, {i, 1, n}]; [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Dec 04 2008]
s = 1; lst = {s}; Do[s += n + 4; AppendTo[lst, s], {n, 1, 200, 3}]; lst [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 11 2009]
Table[Sum[i + n - 3, {i, 1, n}], {n, 2, 50}] [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 11 2009]
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CROSSREFS
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Cf. A005449, A051340, A131414.
A000217 [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 11 2009]
Sequence in context: A028557 A083657 A010740 this_sequence A119867 A026055 A165986
Adjacent sequences: A095791 A095792 A095793 this_sequence A095795 A095796 A095797
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KEYWORD
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nonn
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AUTHOR
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Gary W. Adamson (qntmpkt(AT)yahoo.com), Jun 06 2004, Jul 08 2007
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EXTENSIONS
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Corrected and extended by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jun 23 2006
Comment corrected by Jason Bandlow (jbandlow(AT)math.upenn.edu), Feb 28 2009
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