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1, 3, 8, 16, 27, 41, 58, 78, 101, 127, 156, 188, 223, 261, 302, 346, 393, 443, 496, 552, 611, 673, 738, 806, 877, 951, 1028, 1108, 1191, 1277, 1366, 1458, 1553, 1651, 1752, 1856, 1963, 2073, 2186, 2302, 2421, 2543, 2668, 2796, 2927, 3061, 3198, 3338, 3481
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Second differences are all 3.
Related to the sequence of odd numbers A005408 since for these numbers the first differences are all 2.
Column 2 of A114202. - Paul Barry (pbarry(AT)wit.ie), Nov 17 2005
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 0..3000
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+2*x^2)/(1-x)^3, recurrence: {u(1) = 3, u(2) = 8, (n+3)*u(n+3)+(-5-n)*u(n+2)+(-2+2*n)*u(n+1)+(-2-2*n)*u(n), u(0) = 1}.
a(0)=1, a(n)=a(n-1)+3n-1, n>0; a(n)=sum{k=0..n, C(n, k)C(2, k)J(k+1)}, J(n)=A001045(n). - Paul Barry (pbarry(AT)wit.ie), Nov 17 2005
Equals binomial transform of [1, 2, 3, 0, 0, 0,...]. - Gary W. Adamson (qntmpkt(AT)yahoo.com), Apr 23 2008
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EXAMPLE
| The sequence of first differences delta_a(n) = a(n+1) - a(n) is
2,5,8,11,14,17,20,23,26,...
The sequence of second differences delta_delta_a(n) = a(n+2) - 2*a(n+1) + a(n) is
3,3,3,3,3,3,3,3,3,...
E.g. 78 - 2*58 + 41 = 3.
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MAPLE
| a := proc (n) local i, u; option remember; u[0] := 1; u[1] := 3; u[2] := 8; for i from 3 to n do u[i] := -(4*u[i-3]-8*u[i-2]-2*u[i-1]+(-2*u[i-3]+2*u[i-2]-u[i-1])*i)/i end do; [seq(u[i], i = 0 .. n)] end proc;
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MATHEMATICA
| A104249[n_] := (3*n^2 + n + 2)/2; Table[A104249[n], {n, 0, 100}] (* From Vladimir Joseph Stephan Orlovsky, Jul 22 2011 *)
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PROG
| (MAGMA) [(3*n^2+n+2)/2: n in [0..50]]; // Vincenzo Librandi, May 09 2011
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CROSSREFS
| Cf. A005408, A016777, A002597, A001399.
Contribution from Johannes W. Meijer (meijgia(AT)hotmail.com), Nov 12 2009: (Start)
Equals third row of A167560 divided by 2.
(End)
Sequence in context: A122794 A115006 A122796 * A025202 A131941 A009858
Adjacent sequences: A104246 A104247 A104248 * A104250 A104251 A104252
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KEYWORD
| easy,nonn
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AUTHOR
| Thomas Wieder (wieder.thomas(AT)t-online.de), Feb 26 2005
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