A271740 a(n) = 3*n^2 - 2*n + 2.

2, 3, 10, 23, 42, 67, 98, 135, 178, 227, 282, 343, 410, 483, 562, 647, 738, 835, 938, 1047, 1162, 1283, 1410, 1543, 1682, 1827, 1978, 2135, 2298, 2467, 2642, 2823, 3010, 3203, 3402, 3607, 3818, 4035, 4258, 4487, 4722, 4963, 5210, 5463, 5722, 5987, 6258, 6535, 6818, 7107, 7402, 7703

Offset: 0

Author

Ray Chandler, Apr 13 2016

Keywords

• nonn
• easy

Comments

3*a(n) - 5 is a square. - Vincenzo Librandi, Apr 13 2016

Links

• Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Crossrefs

Cf. A141631, A271713.

Programs

Magma

[3*n^2 - 2*n + 2: n in [0..50]]; // Bruno Berselli, Apr 13 2016

Maple

A271740:=n->3*n^2 - 2*n + 2: seq(A271740(n), n=0..100); # Wesley Ivan Hurt, Apr 13 2016

Mathematica

Table[3 n^2 - 2 n + 2, {n, 0, 50}]

PARI

a(n) = 3*n^2 - 2*n + 2; \\ Altug Alkan, Apr 13 2016

Formula

A271713 = A141631 union A271740.

From Bruno Berselli, Apr 13 2016: (Start)

O.g.f.: (3 + x + 2*x^2)/(1 - x)^3.

E.g.f.: (3 + 7*x + 3*x^2)*exp(x). (End)

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>2. - Wesley Ivan Hurt, Apr 13 2016

Extensions

Definition changed so sequence starts one term earlier. Some formulas may need adjusting. - N. J. A. Sloane, Jun 22 2021