login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A204556 Left edge of the triangle A045975. 5
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 (list; graph; refs; listen; history; text; internal format)
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: A323807 A075714 A101583 * A185669 A294872 A006002

Adjacent sequences:  A204553 A204554 A204555 * A204557 A204558 A204559

KEYWORD

nonn,easy

AUTHOR

Reinhard Zumkeller, Jan 18 2012

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified July 14 16:21 EDT 2020. Contains 335729 sequences. (Running on oeis4.)