A181995 a(n) = if n mod 2 = 1 then n*(n - 1) else (n - 1)^2 + (n - 2)/2.

0, 0, 1, 6, 10, 20, 27, 42, 52, 72, 85, 110, 126, 156, 175, 210, 232, 272, 297, 342, 370, 420, 451, 506, 540, 600, 637, 702, 742, 812, 855, 930, 976, 1056, 1105, 1190, 1242, 1332, 1387, 1482, 1540, 1640, 1701, 1806, 1870, 1980, 2047, 2162, 2232, 2352, 2425, 2550, 2626, 2756, 2835, 2970, 3052, 3192, 3277, 3422, 3510, 3660, 3751, 3906, 4000, 4160, 4257, 4422

Offset: 0

Author

N. J. A. Sloane, Apr 05 2012

Keywords

• nonn
• easy

Comments

Decagonal numbers (A001107) and twice second hexagonal numbers (A002943) interleaved. - Omar E. Pol, Aug 03 2012

Similar to A074377. Members of this family are A093005, A210977, A006578, A210978, this sequence, A210981, A210982. - Omar E. Pol, Aug 09 2012

Number of kites whose vertices are the vertices a regular 2n-gon. - Halil Ibrahim Kanpak, Nov 08 2018

Links

• H. L. Abbott, D. Hanson, N. Sauer, Intersection theorems for systems of sets, J. Combinatorial Theory Ser. A 12 (1972), 381--389.MR0297579 (45 #6633).
• Index entries for linear recurrences with constant coefficients, signature (1,2,-2,-1,1).

Crossrefs

Cf. A001107, A002943, A006578, A074377, A093005.

Cf. A210977, A210978, A210981, A210982.

Programs

Magma

[n*(4*n - 5 - (-1)^n)/4 : n in [0..80]]; // Wesley Ivan Hurt, Apr 11 2016

Maple

f:=n->if n mod 2 = 1 then n*(n-1) else (n-1)^2+(n-2)/2; fi;
[seq(f(n),n=0..130)];

Mathematica

Table[n*(4*n - 5 - (-1)^n)/4, {n, 0, 80}] (* Wesley Ivan Hurt, Apr 11 2016 *)

PARI

a(n)=n*(4*n-5-(-1)^n)/4 \\ Charles R Greathouse IV, Oct 07 2015

Formula

G.f.: -x^2*(1 + 5*x + 2*x^2)/((1 + x)^2*(x - 1)^3). - R. J. Mathar, Apr 06 2012

a(n) = n*(4*n - 5 - (-1)^n)/4. - Luce ETIENNE, Oct 04 2014

From Wesley Ivan Hurt, Apr 11 2016: (Start)

a(n) = a(n-1) + 2*a(n-2) - 2*a(n-3) - a(n-4) + a(n-5) for n>4.

a(n) = Sum_{i=floor((n-1)/2)..floor(3*(n-1)/2)} i. (End)

E.g.f.: x^2*cosh(x) - x*(1 - 2*x)*sinh(x)/2. - Franck Maminirina Ramaharo, Nov 08 2018