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A141631
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3*n^2 - 4*n + 3.
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6
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2, 7, 18, 35, 58, 87, 122, 163, 210, 263, 322, 387, 458, 535, 618, 707, 802, 903, 1010, 1123, 1242, 1367, 1498, 1635, 1778, 1927, 2082, 2243, 2410, 2583, 2762, 2947, 3138, 3335, 3538, 3747, 3962, 4183, 4410, 4643, 4882, 5127, 5378, 5635, 5898, 6167, 6442
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OFFSET
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1,1
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COMMENTS
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First bisection of A133146.
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LINKS
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Table of n, a(n) for n=1..47.
Index entries for linear recurrences with constant coefficients, signature (3, -3, 1).
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FORMULA
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a(n) = A133146(2n-2) = (n-2)^2+(n-1)(n+1)+n^2.
First differences: a(n+1)-a(n) = A016969(n-1).
G.f.: x*(2+x+3*x^2) / (1-x)^3. - R. J. Mathar, Oct 15 2008
a(n) = 6*n+a(n-1)-7, with n>1, a(1)=2. - Vincenzo Librandi, Nov 25 2010
a(n) = 2*A000290(n)^2 + A067998(n-1) = 2*n^2+(n-1)*(n-3). - L. Edson Jeffery, Nov 30 2013
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MATHEMATICA
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s=2; lst={s}; Do[s+=n+5; AppendTo[lst, s], {n, 0, 6!, 6}]; lst (* Vladimir Joseph Stephan Orlovsky, Nov 04 2008 *)
Table[3 n^2 - 4 n + 3, {n, 50}] (* Harvey P. Dale, Oct 28 2012 *)
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PROG
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(PARI) a(n)=3*n^2-4*n+3 \\ Charles R Greathouse IV, Jun 17 2017
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CROSSREFS
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Cf. A000004 (third differences), A010722 (second differences).
Sequence in context: A195605 A184096 A136583 * A172188 A077131 A212685
Adjacent sequences: A141628 A141629 A141630 * A141632 A141633 A141634
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KEYWORD
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nonn,less,easy
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AUTHOR
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Paul Curtz, Aug 28 2008
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EXTENSIONS
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Edited and extended by R. J. Mathar, Oct 15 2008
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STATUS
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approved
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