A195323 a(n) = 22*n^2.

0, 22, 88, 198, 352, 550, 792, 1078, 1408, 1782, 2200, 2662, 3168, 3718, 4312, 4950, 5632, 6358, 7128, 7942, 8800, 9702, 10648, 11638, 12672, 13750, 14872, 16038, 17248, 18502, 19800, 21142, 22528, 23958, 25432, 26950, 28512, 30118, 31768, 33462, 35200, 36982, 38808

Offset: 0

Author

Omar E. Pol, Sep 16 2011

Keywords

• nonn
• easy

Comments

Sequence found by reading the line from 0, in the direction 0, 22, ..., in the square spiral whose vertices are the generalized tridecagonal numbers A195313. Semi-axis opposite to A195318 in the same spiral.

Surface area of a rectangular prism with dimensions n, 2n and 3n. - Wesley Ivan Hurt, Apr 10 2015

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

Bisection of A195149.

Cf. A016802, A033581, A033583, A135453, A139098, A144555, A195321, A195322.

Cf. A000290, A001105, A008604, A033584, A195313, A195318.

Programs

Magma

[22*n^2 : n in [0..40]]; // Vincenzo Librandi, Sep 20 2011

Maple

A195323:=n->22*n^2: seq(A195323(n), n=0..80); # Wesley Ivan Hurt, Apr 10 2015

Mathematica

22Range[0,50]^2 (* or *) LinearRecurrence[{3,-3,1},{0,22,88},50] (* Harvey P. Dale, Sep 19 2011 *)

PARI

vector(50,n,22*(n-1)^2) \\ Derek Orr, Apr 10 2015

Formula

a(n) = 22*A000290(n) = 11*A001105(n) = 2*A033584(n).

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - Harvey P. Dale, Sep 19 2011

G.f.: 22*x*(1+x)/(1-x)^3. - Wesley Ivan Hurt, Apr 10 2015

From Elmo R. Oliveira, Dec 01 2024: (Start)

E.g.f.: 22*x*(1 + x)*exp(x).

a(n) = n*A008604(n) = A195149(2*n). (End)