A026043 a(n) = dot_product(1,2,...,n)*(5,6,...,n,1,2,3,4).

45, 67, 98, 140, 195, 265, 352, 458, 585, 735, 910, 1112, 1343, 1605, 1900, 2230, 2597, 3003, 3450, 3940, 4475, 5057, 5688, 6370, 7105, 7895, 8742, 9648, 10615, 11645, 12740, 13902, 15133, 16435, 17810, 19260, 20787, 22393, 24080, 25850, 27705

Offset

5,1

Links

Vincenzo Librandi, Table of n, a(n) for n = 5..1000

Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Formula

a(n) = n(2n^2 - 9n + 49)/6 (n >= 5). - Emeric Deutsch, Nov 29 2006

G.f.: x^5*(45 - 113*x + 100*x^2 - 30*x^3)/(1 - x)^4. - Colin Barker, Sep 17 2012

Maple

a:=n->n*(2*n^2-9*n+49)/6: seq(a(n), n=5..45); # Emeric Deutsch, Nov 29 2006

Mathematica

Table[Range[n].RotateLeft[Range[n], 4], {n, 5, 51}] (* T. D. Noe, Nov 07 2006 *)
CoefficientList[Series[(45 - 113 x + 100 x^2 - 30 x^3)/(1 - x)^4, {x, 0, 60}], x] (* Vincenzo Librandi, Oct 17 2013 *)

Prog

(Magma) [n*(2*n^2-9*n+49)/6: n in [5..60]]; // Vincenzo Librandi, Oct 17 2013

Crossrefs

Column 4 of triangle A094414.

Sequence in context: A056776 A172466 A038494 * A330850 A053720 A259218

Adjacent sequences: A026040 A026041 A026042 * A026044 A026045 A026046

Keyword

nonn,easy

Author

Clark Kimberling

Extensions

Corrected by T. D. Noe, Nov 07 2006

Status

approved