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

1,2

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).

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)

Mathematica

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

Prog

(Haskell)
a204556 = head . a045975_row
(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
(Magma) [n*(2*n^2-3*n+(-1)^n*(n-3)+3)/4: n in [1..50]]; // G. C. Greubel, Jun 15 2018

Crossrefs

Sequence in context: A075714 A101583 A339923 * A185669 A360518 A294872

Adjacent sequences: A204553 A204554 A204555 * A204557 A204558 A204559

Keyword

nonn,easy

Author

Reinhard Zumkeller, Jan 18 2012

Status

approved