A204556 Left edge of the triangle A045975.

1, 2, 9, 24, 45, 90, 133, 224, 297, 450, 561, 792, 949, 1274, 1485, 1920, 2193, 2754, 3097, 3800, 4221, 5082, 5589, 6624, 7225, 8450, 9153, 10584, 11397, 13050, 13981, 15872, 16929, 19074, 20265, 22680, 24013, 26714, 28197, 31200, 32841, 36162, 37969, 41624

Offset: 1

Author

Reinhard Zumkeller, Jan 18 2012

Keywords

• nonn
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 1..5000
• Index entries for linear recurrences with constant coefficients, signature (1,3,-3,-3,3,1,-1).

Programs

Haskell

a204556 = head . a045975_row

Magma

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

Mathematica

Table[n*(2*n^2 - 3*n + (-1)^n*(n - 3) + 3)/4, {n, 1, 50}] (* G. C. Greubel, Jun 15 2018 *)

PARI

Vec(x*(1+x+4*x^2+12*x^3+3*x^4+3*x^5)/((1+x)^3*(x-1)^4) + O(x^99)) \\ Charles R Greathouse IV, Jun 12 2015

PARI

for(n=1, 50, print1(n*(2*n^2-3*n+(-1)^n*(n-3)+3)/4, ", ")) \\ G. C. Greubel, Jun 15 2018

Formula

a(n) = A045975(n,1);

a(n) = A031940(n-1) * n for n > 1;

a(n) = A204557(n) - A045895(n).

G.f.: x*(1+x+4*x^2+12*x^3+3*x^4+3*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*n+(-1)^n*(n-3)+3)/4.

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

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

(End)