A341209 a(n) = (n^3 + 6*n^2 + 17*n + 6)/6.

1, 5, 12, 23, 39, 61, 90, 127, 173, 229, 296, 375, 467, 573, 694, 831, 985, 1157, 1348, 1559, 1791, 2045, 2322, 2623, 2949, 3301, 3680, 4087, 4523, 4989, 5486, 6015, 6577, 7173, 7804, 8471, 9175, 9917, 10698, 11519, 12381, 13285, 14232, 15223, 16259, 17341, 18470, 19647

Offset

0,2

Comments

a(1) = A339400(7) = A339400(11), a(2) = A339756(7) = A339756(11), a(3) = A339947(7) = A339947(11).

Conjecture: Mark each point on a 7^k or 11^k grid with the number of points that are visible from the point; for n > 0, a(n) is the number of distinct values in both grids.

Links

Table of n, a(n) for n=0..47.

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

Formula

a(n) = (n^3 + 6*n^2 + 17*n + 6)/6.

a(n) = A004006(n+2) - 2, n > 0.

From Elmo R. Oliveira, May 22 2026: (Start)

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

E.g.f.: exp(x)*(6 + 24*x + 9*x^2 + x^3)/6.

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

a(n) = A033547(n+1) - A050407(n+2). (End)

Prog

(PARI) a(n) = (n^3 + 6*n^2 + 17*n + 6)/6;

Crossrefs

Cf. A004006, A033547, A050407, A339400, A339756, A339947.

Sequence in context: A172295 A332569 A126573 * A000327 A220425 A130624

Adjacent sequences: A341206 A341207 A341208 * A341210 A341211 A341212

Keyword

nonn,easy

Author

Torlach Rush, Feb 06 2021

Status

approved