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

1,2

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).

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)

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 *)

Prog

(Haskell)
a204557 = last . a045975_row
(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
(Magma) [n*(2*n^2+(3-(-1)^n)*n-(-1)^n-3)/4: n in [1..50]]; // G. C. Greubel, Jun 15 2018

Crossrefs

Sequence in context: A273699 A273707 A364679 * A161444 A188219 A280091

Adjacent sequences: A204554 A204555 A204556 * A204558 A204559 A204560

Keyword

nonn,easy

Author

Reinhard Zumkeller, Jan 18 2012

Status

approved