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

Author

N. J. A. Sloane

Keywords

• nonn
• easy
• changed

Links

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

Crossrefs

Cf. A047666, A192793.

Programs

PARI

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

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)

Extensions

More terms from Elmo R. Oliveira, Aug 26 2025