A195018 a(n) = n*(10*n-3).

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.

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..10000

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

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.

Cf. A000566, A033571, A085787, A195013, A195014, A195015, A153127.

Sequence in context: A117663 A063166 A259055 * A024817 A201230 A071598

Adjacent sequences: A195015 A195016 A195017 * A195019 A195020 A195021

Keyword

nonn,easy

Author

Omar E. Pol, Oct 14 2011

Status

approved