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A195018
a(n) = n*(10*n-3).
2
0, 7, 34, 81, 148, 235, 342, 469, 616, 783, 970, 1177, 1404, 1651, 1918, 2205, 2512, 2839, 3186, 3553, 3940, 4347, 4774, 5221, 5688, 6175, 6682, 7209, 7756, 8323, 8910, 9517, 10144, 10791, 11458, 12145, 12852, 13579, 14326, 15093, 15880, 16687, 17514, 18361, 19228
OFFSET
0,2
COMMENTS
Bisection of heptagonal numbers A000566.
Sequence found by reading the line from 0, in the direction 0, 7, ..., in the square spiral whose vertices are the generalized heptagonal numbers A085787. This is one of the four semi-diagonals of the square spiral.
Also sequence found by reading the line from 0, in the direction 0, 7, ..., in the square spiral whose edges have length A195013 and whose vertices are the numbers A195014. Semi-axis perpendicular to the main axis A195015 in the same spiral.
FORMULA
a(n) = A153127(n-1) + 1, if n >= 1.
G.f.: -x*(7+13*x)/(x-1)^3. - R. J. Mathar, Oct 15 2011
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3); a(0)=0, a(1)=7, a(2)=34. - Harvey P. Dale, May 27 2012
From Elmo R. Oliveira, Dec 15 2024: (Start)
E.g.f.: exp(x)*x*(7 + 10*x).
a(n) = A000566(2*n). (End)
MATHEMATICA
Table[n (10 n-3), {n, 0, 50}] (* or *) LinearRecurrence[{3, -3, 1}, {0, 7, 34}, 50] (* Harvey P. Dale, May 27 2012 *)
PROG
(Magma) [n*(10*n-3): n in [0..50]]; // Vincenzo Librandi, Oct 28 2011
(PARI) a(n)=n*(10*n-3) \\ Charles R Greathouse IV, Jun 17 2017
CROSSREFS
Also bisection of A195016.
Sequence in context: A117663 A063166 A259055 * A024817 A201230 A071598
KEYWORD
nonn,easy
AUTHOR
Omar E. Pol, Oct 14 2011
STATUS
approved