Search: id:A095794
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%I A095794
%S A095794 1,6,14,25,39,56,76,99,125,154,186,221,259,300,344,391,441,494,550,609,
%T A095794 671,736,804,875,949,1026,1106,1189,1275,1364,1456,1551,1649,1750,1854,
%U A095794 1961,2071,2184,2300,2419,2541,2666,2794,2925,3059,3196,3336,3479,3625
%N A095794 a(n) = A005449(n) - 1, where A005449 = second pentagonal numbers.
%C A095794 a(n) = A126890(n+1,n-2) for n>1. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), 
               Dec 30 2006
%F A095794 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].
%F A095794 sum (n+j-1,j=0..n). - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Sep 12 2006
%F A095794 Row sums of triangle A131414.
%F A095794 Equals binomial transform of (1, 5, 3, 0, 0, 0,...). Equals A051340 * 
               (1, 2, 3,...).
%F A095794 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
%F A095794 a(n)=3*n+a(n-1)-1 (with a(1)=1) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), 
               Nov 08 2009]
%e A095794 1. a(4) = 25 = A005449(4) - 1
%e A095794 2. a(5) = 39 = f(n), n=5 in (3/2)n^2 + (1/2)n - 1.
%e A095794 3. a(7) = 76 = 3*56 - 3*39 + 25
%e A095794 4. a(5) = 39 = right term of M^4 * [1 1 1] = [1 5 39].
%e A095794 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]
%p A095794 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
%p A095794 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
%t A095794 a[n_]:=Sum[i+n-3, {i, 1, n}]; [From Vladimir Orlovsky (4vladimir(AT)gmail.com), 
               Dec 04 2008]
%t A095794 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]
%t A095794 Table[Sum[i + n - 3, {i, 1, n}], {n, 2, 50}] [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Jul 11 2009]
%Y A095794 Cf. A005449, A051340, A131414.
%Y A095794 A000217 [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 11 2009]
%Y A095794 Sequence in context: A028557 A083657 A010740 this_sequence A119867 A026055 
               A165986
%Y A095794 Adjacent sequences: A095791 A095792 A095793 this_sequence A095795 A095796 
               A095797
%K A095794 nonn,new
%O A095794 1,2
%A A095794 Gary W. Adamson (qntmpkt(AT)yahoo.com), Jun 06 2004, Jul 08 2007
%E A095794 Corrected and extended by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), 
               Jun 23 2006
%E A095794 Comment corrected by Jason Bandlow (jbandlow(AT)math.upenn.edu), Feb 
               28 2009

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