A027621 a(n) = n + (n+1)^2 + (n+2)^3 + (n+3)^4.

90, 288, 700, 1440, 2646, 4480, 7128, 10800, 15730, 22176, 30420, 40768, 53550, 69120, 87856, 110160, 136458, 167200, 202860, 243936, 290950, 344448, 405000, 473200, 549666, 635040, 729988, 835200, 951390, 1079296, 1219680

Offset

0,1

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..10000

Patrick De Geest, Palindromic Quasi_Under_Squares of the form n+(n+1)^2

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

Formula

G.f.: 16/(1-x) + 16/(1-x)^2 + 16/(1-x)^3 + 18/(1-x)^4 + 24/(1-x)^5. - R. J. Mathar, Feb 22 2008

a(n) = (n+3)^2*(n^2 + 7*n + 10). - Bruno Berselli, Aug 05 2011

E.g.f.: (90 + 198*x + 107*x^2 + 19*x^3 + x^4)*exp(x). - G. C. Greubel, Aug 05 2022

Maple

seq( (n+3)^2*(n^2 + 7*n + 10), n=0..40); # G. C. Greubel, Aug 05 2022

Mathematica

Table[Total[Table[(n+i)^(i+1), {i, 0, 3}]], {n, 0, 40}] (* or *) LinearRecurrence[ {5, -10, 10, -5, 1}, {90, 288, 700, 1440, 2646}, 40] (* Harvey P. Dale, Jun 08 2017 *)

Prog

(Sage) [i+(i+1)^2+(i+2)^3+(i+3)^4 for i in range(0, 40)] # Zerinvary Lajos, Jul 03 2008
(Magma) [n + (n+1)^2 + (n+2)^3 + (n+3)^4: n in [0..40]]; // Vincenzo Librandi, Aug 05 2011

Crossrefs

Cf. A000027, A027620, A027622, A028387.

Sequence in context: A255784 A250877 A250878 * A331259 A245866 A157888

Adjacent sequences: A027618 A027619 A027620 * A027622 A027623 A027624

Keyword

nonn,easy

Author

Patrick De Geest

Status

approved