A071229 a(n) = n*(14*n^2 - 21*n + 13)/6.

0, 1, 9, 38, 102, 215, 391, 644, 988, 1437, 2005, 2706, 3554, 4563, 5747, 7120, 8696, 10489, 12513, 14782, 17310, 20111, 23199, 26588, 30292, 34325, 38701, 43434, 48538, 54027, 59915, 66216, 72944, 80113, 87737, 95830, 104406, 113479, 123063

Offset

0,3

References

T. A. Gulliver, Sequences from Arrays of Integers, Int. Math. Journal, Vol. 1, No. 4, pp. 323-332, 2002.

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..2000

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

Formula

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

G.f.: x*(1 + 5*x + 8*x^2)/(1-x)^4. - Harvey P. Dale, Jun 29 2011

E.g.f.: (1/6)*x*(6 + 21*x + 14*x^2)*exp(x). - G. C. Greubel, Aug 05 2024

Mathematica

Table[ n*(14*n^2 - 21*n + 13)/6, {n, 0, 40}]
LinearRecurrence[{4, -6, 4, -1}, {0, 1, 9, 38}, 40] (* or *) CoefficientList[ Series[x*(1+5x+8x^2)/(1-x)^4, {x, 0, 40}], x] (* Harvey P. Dale, Jun 29 2011 *)

Prog

(Magma) [n*(14*n^2-21*n+13)/6: n in [0..50]]; // Vincenzo Librandi, Jun 14 2011
(SageMath)
def A071229(n): return n*(14*n^2-21*n+13)/6
[A071229(n) for n in range(51)] # G. C. Greubel, Aug 05 2024

Crossrefs

Sequence in context: A076174 A117085 A120780 * A071238 A213583 A343521

Adjacent sequences: A071226 A071227 A071228 * A071230 A071231 A071232

Keyword

nonn,easy

Author

N. J. A. Sloane, Jun 11 2002

Extensions

More terms from Robert G. Wilson v, Jun 12 2002

Status

approved