A047667 Row 3 of array in A047666.

3, 10, 25, 52, 95, 158, 245, 360, 507, 690, 913, 1180, 1495, 1862, 2285, 2768, 3315, 3930, 4617, 5380, 6223, 7150, 8165, 9272, 10475, 11778, 13185, 14700, 16327, 18070, 19933, 21920, 24035, 26282, 28665, 31188, 33855, 36670, 39637, 42760, 46043, 49490, 53105

Offset

1,1

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

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

Formula

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

From Elmo R. Oliveira, Aug 26 2025: (Start)

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

E.g.f.: x*(9 + 6*x + 2*x^2)*exp(x)/3.

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

a(n) = A192793(n)/36. (End)

Mathematica

LinearRecurrence[{4, -6, 4, -1}, {3, 10, 25, 52}, 50] (* Harvey P. Dale, Jan 18 2026 *)

Prog

(PARI) my(x='x+O('x^44)); Vec(x*(3-2*x+3*x^2)/(x-1)^4) \\ Elmo R. Oliveira, Aug 26 2025

Crossrefs

Cf. A047666, A192793.

Sequence in context: A212068 A162607 A267574 * A192963 A000247 A097763

Adjacent sequences: A047664 A047665 A047666 * A047668 A047669 A047670

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

More terms from Elmo R. Oliveira, Aug 26 2025

Status

approved