A204557 Right edge of the triangle A045975.

1, 4, 21, 36, 85, 120, 217, 280, 441, 540, 781, 924, 1261, 1456, 1905, 2160, 2737, 3060, 3781, 4180, 5061, 5544, 6601, 7176, 8425, 9100, 10557, 11340, 13021, 13920, 15841, 16864, 19041, 20196, 22645, 23940, 26677, 28120, 31161, 32760, 36121, 37884, 41581

Offset: 1

Author

Reinhard Zumkeller, Jan 18 2012

Keywords

• nonn
• easy

Links

• Colin Barker, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (1,3,-3,-3,3,1,-1).

Programs

Haskell

a204557 = last . a045975_row

Magma

[n*(2*n^2+(3-(-1)^n)*n-(-1)^n-3)/4: n in [1..50]]; // G. C. Greubel, Jun 15 2018

Mathematica

Table[n*(2*n^2+(3-(-1)^n)*n-(-1)^n-3)/4, {n, 1, 50}] (* G. C. Greubel, Jun 15 2018 *)
LinearRecurrence[{1,3,-3,-3,3,1,-1},{1,4,21,36,85,120,217},50] (* Harvey P. Dale, Feb 20 2021 *)

PARI

Vec(-x*(-1-3*x-14*x^2-6*x^3-x^4+x^5)/((1+x)^3*(x-1)^4) + O(x^100)) \\ Colin Barker, Jan 28 2016

Formula

a(n) = A045975(n,n);

a(n) = A079326(n+1) * n;

a(n) = A204556(n) + A045895(n).

G.f.: -x*(-1-3*x-14*x^2-6*x^3-x^4+x^5) / ((1+x)^3*(x-1)^4). - R. J. Mathar, Aug 13 2012

From Colin Barker, Jan 28 2016: (Start)

a(n) = n*(2*n^2+(3-(-1)^n)*n-(-1)^n-3)/4.

a(n) = (n^3+n^2-2*n)/2 for n even.

a(n) = (n^3+2*n^2-n)/2 for n odd.

(End)