A055437 a(n) = 10*n^2+n.

11, 42, 93, 164, 255, 366, 497, 648, 819, 1010, 1221, 1452, 1703, 1974, 2265, 2576, 2907, 3258, 3629, 4020, 4431, 4862, 5313, 5784, 6275, 6786, 7317, 7868, 8439, 9030, 9641, 10272, 10923, 11594, 12285, 12996, 13727, 14478, 15249, 16040, 16851, 17682, 18533

Offset: 1

Author

Henry Bottomley, May 18 2000

Keywords

• nonn
• easy

Comments

a(n) = A055436(n) if 1<=n<10.

Number of edges in the join of the complete 4-partite graph of order 4n and the cycle graph of order n, K_n,n,n,n * C_n. - Roberto E. Martinez II, Jan 07 2002

Examples

			From the third formula: a(8) = 648 = 16^2 -17^2 +18^2 ... +30^2 -31^2 +32^2 = -33^2 +34^2 -35^2 ... +46^2 -47^2 +48^2.
		

Links

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

Crossrefs

Cf. A000217, A002378, A055436, A055438.

Programs

Magma

[10*n^2+n : n in [1..50]]; // Wesley Ivan Hurt, Apr 27 2016

Maple

A055437:=n->10*n^2+n: seq(A055437(n), n=1..50); # Wesley Ivan Hurt, Apr 27 2016

Mathematica

Table[10 n^2 + n, {n, 50}] (* Wesley Ivan Hurt, Apr 27 2016 *)

PARI

a(n)=10*n^2+n \\ Charles R Greathouse IV, Jun 17 2017

Formula

From Bruno Berselli, Nov 26 2013: (Start)

G.f.: x*(11 + 9*x) / (1 - x)^3.

a(n) = Sum_{i=0..2*n} (-1)^i*(2*n+i)^2.

a(n) = Sum_{i=1..2*n} (-1)^i*(4*n+i)^2. (End)

From Wesley Ivan Hurt, Apr 27 2016: (Start)

a(n) = 3*a(n-1)-3*a(n-2)+a(n-3) for n>3.

a(n) = (1/5) * Sum_{i=0..10*n} i. (End)

E.g.f.: x*(11 + 10*x)*exp(x). - Ilya Gutkovskiy, Apr 27 2016

a(n) = A000217(6*n) - A000217(4*n). - Bruno Berselli, Sep 21 2016