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

Author

Omar E. Pol, Oct 14 2011

Keywords

• nonn
• easy

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).

Crossrefs

Also bisection of A195016.

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

Programs

Magma

[n*(10*n-3): n in [0..50]]; // Vincenzo Librandi, Oct 28 2011

Mathematica

Table[n (10 n-3),{n,0,50}] (* or *) LinearRecurrence[{3,-3,1},{0,7,34},50] (* Harvey P. Dale, May 27 2012 *)

PARI

a(n)=n*(10*n-3) \\ Charles R Greathouse IV, Jun 17 2017

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)