A071230 a(n) = n*(6*n^2 - 7*n + 3)/2.

0, 1, 13, 54, 142, 295, 531, 868, 1324, 1917, 2665, 3586, 4698, 6019, 7567, 9360, 11416, 13753, 16389, 19342, 22630, 26271, 30283, 34684, 39492, 44725, 50401, 56538, 63154, 70267, 77895, 86056, 94768, 104049, 113917, 124390, 135486

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) - a(n-4).

From G. C. Greubel, Aug 05 2024: (Start)

G.f.: x*(1 + 9*x + 8*x^2)/(1-x)^4.

E.g.f.: (1/2)*x*(2 + 11*x + 6*x^2)*exp(x). (End)

Mathematica

Table[n*(6*n^2 - 7*n + 3)/2, {n, 0, 40}]
LinearRecurrence[{4, -6, 4, -1}, {0, 1, 13, 54}, 40] (* Harvey P. Dale, May 29 2025 *)

Prog

(Magma) [n*(6*n^2-7*n+3)/2: n in [0..50]]; // Vincenzo Librandi, Jun 14 2011
(SageMath)
def A071230(n): return n*(6*n^2 -7*n +3)//2
[A071230(n) for n in range(51)] # G. C. Greubel, Aug 05 2024

Crossrefs

Cf. A071229.

Sequence in context: A358166 A372756 A195024 * A027000 A198160 A029531

Adjacent sequences: A071227 A071228 A071229 * A071231 A071232 A071233

Keyword

nonn,easy

Author

N. J. A. Sloane, Jun 11 2002

Extensions

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

Status

approved