A298375 Partial sums of A230584.

2, 5, 11, 18, 29, 43, 61, 84, 111, 145, 183, 230, 281, 343, 409, 488, 571, 669, 771, 890, 1013, 1155, 1301, 1468, 1639, 1833, 2031, 2254, 2481, 2735, 2993, 3280, 3571, 3893, 4219, 4578, 4941, 5339, 5741, 6180, 6623, 7105, 7591, 8118, 8649, 9223, 9801, 10424

Offset: 1

Author

Gerald Hillier, Jan 18 2018

Keywords

• nonn
• easy

Examples

			For n = 5 then a(5) = 2+3+6+7+11 = 29.
		

Links

• Colin Barker, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (2,1,-4,1,2,-1).

Crossrefs

Cf. A230584.

Programs

Mathematica

CoefficientList[ Series[(2 + x - x^2 - x^3 + 2x^5 - x^6)/((x -1)^4 (x + 1)^2), {x, 0, 50}], x] (* Robert G. Wilson v, Jan 18 2018 *)

PARI

Vec(x*(2 + x - x^2 - x^3 + 2*x^5 - x^6) / ((1 - x)^4*(1 + x)^2) + O(x^50)) \\ Colin Barker, Jan 18 2018

Formula

Let g = n + ((n + 1) mod 2), then for n > 1,

a(n) = (g^3 + 6*g^2 + 11*g + 18) / 12 - If(n mod 2 = 1, 0, ((n + 2) / 2)^2 + 2).

From Colin Barker, Jan 18 2018: (Start)

G.f.: x*(2 + x - x^2 - x^3 + 2*x^5 - x^6) / ((1 - x)^4*(1 + x)^2).

a(n) = (n^3 + 6*n^2 + 14*n) / 12 for n>1 and even.

a(n) = (n^3 + 6*n^2 + 11*n + 18) / 12 for n>1 and odd.

a(n) = 2*a(n-1) + a(n-2) - 4*a(n-3) + a(n-4) + 2*a(n-5) - a(n-6) for n>6.

(End)