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A102083
a(n) = 8*n^2 + 4*n + 1.
14
1, 13, 41, 85, 145, 221, 313, 421, 545, 685, 841, 1013, 1201, 1405, 1625, 1861, 2113, 2381, 2665, 2965, 3281, 3613, 3961, 4325, 4705, 5101, 5513, 5941, 6385, 6845, 7321, 7813, 8321, 8845, 9385, 9941, 10513, 11101, 11705, 12325, 12961, 13613, 14281, 14965, 15665
OFFSET
0,2
COMMENTS
If Y and Z are 2-blocks of a 2n-set X then, for n>=2, a(n-2) is the number of 4-subsets of X intersecting both Y and Z. - Milan Janjic, Nov 18 2007
Equals binomial transform of [1, 12, 16, 0, 0, 0, ...]. - Gary W. Adamson, Jul 19 2008
Sequence found by reading the line from 1, in the direction 1, 13, ..., in the square spiral whose vertices are the triangular numbers A000217. - Omar E. Pol, Sep 05 2011
First differences of A100157. - John Molokach, Jul 10 2013
FORMULA
G.f.: (1+10*x+5*x^2)/(1-x)^3. - Paul Barry, Jun 04 2005
a(n) = 4*(4*n-1)+a(n-1) (with a(0)=1). - Vincenzo Librandi, Nov 16 2010
E.g.f.: (8*x^2 + 12*x + 1)*exp(x). - G. C. Greubel, Jul 14 2017
MATHEMATICA
Table[8*n^2 + 4*n + 1, {n, 0, 300}] (* or *) LinearRecurrence[{3, -3, 1}, {1, 13, 41}, 80] (* Vladimir Joseph Stephan Orlovsky, Feb 17 2012 *)
PROG
(PARI) a(n)=8*n^2+4*n+1 \\ Charles R Greathouse IV, Oct 07 2015
CROSSREFS
Sequence in context: A043942 A004624 A045473 * A139866 A026918 A123972
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Feb 14 2005
STATUS
approved