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

Author

N. J. A. Sloane, May 31 2009

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A154685, A162261.

Programs

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

Mathematica

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

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

Extensions

Extended by R. J. Mathar, May 31 2009