A151675 Row sums of A154685.

8, 27, 63, 122, 210, 333, 497, 708, 972, 1295, 1683, 2142, 2678, 3297, 4005, 4808, 5712, 6723, 7847, 9090, 10458, 11957, 13593, 15372, 17300, 19383, 21627, 24038, 26622, 29385, 32333, 35472, 38808, 42347, 46095, 50058, 54242, 58653, 63297

Offset

1,1

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

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

Formula

From R. J. Mathar, May 31 2009: (Start)

a(n) = n*(2*n^2 + 5*n + 9)/2.

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4).

G.f.: x*(8 - 5*x + 3*x^2)/(1-x)^4. (End)

a(n) = A162261(n) + 8*n. - L. Edson Jeffery, Oct 12 2012

E.g.f.: (1/2)*x*(16 + 11*x + 2*x^2)*exp(x). - G. C. Greubel, Jan 21 2025

Mathematica

CoefficientList[Series[(8-5*x+3*x^2)/(1-x)^4, {x, 0, 40}], x] (* Vincenzo Librandi, Jun 30 2012 *)

Prog

(Magma) I:=[8, 27, 63, 122]; [n le 4 select I[n] else 4*Self(n-1)-6*Self(n-2)+4*Self(n-3)-Self(n-4): n in [1..50]]; // Vincenzo Librandi, Jun 30 2012
(Python)
def A151675(n): return n*(2*n**2 +5*n+9)//2
print([A151675(n) for n in range(1, 51)]) # G. C. Greubel, Jan 21 2025

Crossrefs

Cf. A154685, A162261.

Sequence in context: A141227 A224134 A213488 * A211641 A062686 A093322

Adjacent sequences: A151672 A151673 A151674 * A151676 A151677 A151678

Keyword

nonn,easy

Author

N. J. A. Sloane, May 31 2009

Extensions

Extended by R. J. Mathar, May 31 2009

Status

approved