A058310 (1/2)*(n^2+n+2)*(n^2+3*n+1).

1, 10, 44, 133, 319, 656, 1210, 2059, 3293, 5014, 7336, 10385, 14299, 19228, 25334, 32791, 41785, 52514, 65188, 80029, 97271, 117160, 139954, 165923, 195349, 228526, 265760, 307369, 353683, 405044, 461806, 524335, 593009, 668218, 750364, 839861, 937135

Offset

0,2

Links

Table of n, a(n) for n=0..36.

Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Formula

a(n) = sum(i, i = n..(n+1)^2).

G.f.: (1+5*x+4*x^2+3*x^3-x^4)/(1-x)^5; a(n) = 5*a(n-1)-10*a(n-2)+10*a(n-3)-5*a(n-4)+a(n-5). - Wesley Ivan Hurt, Sep 14 2014

Maple

A058310:=n->(n^2+n+2)*(n^2+3*n+1)/2: seq(A058310(n), n=0..40); # Wesley Ivan Hurt, Sep 14 2014

Mathematica

Table[(n^2 + n + 2) (n^2 + 3 n + 1)/2, {n, 0, 40}] (* Wesley Ivan Hurt, Sep 14 2014 *)
CoefficientList[Series[(1 + 5 x + 4 x^2 + 3 x^3 - x^4)/(1 - x)^5, {x, 0, 30}], x] (* Wesley Ivan Hurt, Sep 14 2014 *)

Prog

(Magma) [(n^2+n+2)*(n^2+3*n+1)/2 : n in [0..40]]; // Wesley Ivan Hurt, Sep 14 2014
(PARI) Vec((1+5*x+4*x^2+3*x^3-x^4)/(1-x)^5 + O(x^50)) \\ Michel Marcus, Sep 15 2014

Crossrefs

Sequence in context: A257052 A008532 A085582 * A005720 A060326 A200448

Adjacent sequences: A058307 A058308 A058309 * A058311 A058312 A058313

Keyword

nonn,easy

Author

N. J. A. Sloane, Dec 09 2000

Extensions

More terms from Wesley Ivan Hurt, Sep 14 2014

Status

approved