A298027 Partial sums of A298026.

1, 7, 13, 31, 43, 73, 91, 133, 157, 211, 241, 307, 343, 421, 463, 553, 601, 703, 757, 871, 931, 1057, 1123, 1261, 1333, 1483, 1561, 1723, 1807, 1981, 2071, 2257, 2353, 2551, 2653, 2863, 2971, 3193, 3307, 3541, 3661, 3907, 4033, 4291, 4423, 4693, 4831, 5113, 5257, 5551, 5701, 6007, 6163, 6481

Offset: 0

Author

N. J. A. Sloane, Jan 21 2018

Keywords

• nonn

Links

• Robert Israel, Table of n, a(n) for n = 0..10000
• Index entries for linear recurrences with constant coefficients, signature (1,2,-2,-1,1).

Crossrefs

Cf. A298026.

Programs

Maple

seq((4+6*n+9*n^2+(3+6*n)*(n mod 2))/4, n=0..100); # Robert Israel, Jan 21 2018

Mathematica

Sort[Table[9 m^2 + 3 m + 1, {m, -20, 20}]] (* Greg Dresden, Jul 02 2018 *)
Accumulate[LinearRecurrence[{0,2,0,-1},{1,6,6,18,12},80]] (* Harvey P. Dale, Oct 02 2020 *)

Formula

From Robert Israel, Jan 21 2018: (Start)

G.f.: (1+6*x+4*x^2+6*x^3+x^4)/((1+x)^2*(1-x)^3).

a(n) = (4+6*n+9*n^2)/4 if n is even, (7+12*n+9*n^2)/4 if n is odd. (End)

Sequence equals values of 9m^2 + 3m + 1 for m = 0, -1, 1, -2, 2, -3, 3, ... . - Greg Dresden, Jul 02 2018