A298030 Partial sums of A298029.

1, 4, 10, 22, 40, 73, 112, 163, 220, 289, 364, 451, 544, 649, 760, 883, 1012, 1153, 1300, 1459, 1624, 1801, 1984, 2179, 2380, 2593, 2812, 3043, 3280, 3529, 3784, 4051, 4324, 4609, 4900, 5203, 5512, 5833, 6160, 6499, 6844, 7201, 7564, 7939, 8320, 8713, 9112, 9523, 9940, 10369, 10804, 11251, 11704

Offset: 0

Author

N. J. A. Sloane, Jan 21 2018

Keywords

• nonn
• easy

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (2,0,-2,1).

Crossrefs

Cf. A298029.

Programs

Mathematica

LinearRecurrence[{2,0,-2,1},{1,4,10,22,40,73,112,163},60] (* Harvey P. Dale, Jul 17 2025 *)

PARI

Vec((1 + 2*x + 2*x^2 + 4*x^3 + 3*x^4 + 9*x^5 - 3*x^7) / ((1 - x)^3*(1 + x)) + O(x^50)) \\ Colin Barker, Jan 25 2018

Formula

G.f.: -(3*x^7 - 9*x^5 - 3*x^4 - 4*x^3 - 2*x^2 - 2*x - 1)/((1 - x)^2*(1 - x^2)).

From Colin Barker, Jan 25 2018: (Start)

a(n) = (9*n^2 - 18*n + 8) / 2 for n>3 and even.

a(n) = (9*n^2 - 18*n + 11) / 2 for n>3 and odd.

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

E.g.f.: ((8 - 9*x + 9*x^2)*cosh(x) + (11 - 9*x + 9*x^2)*sinh(x) - 6 + 6*x + 6*x^2 + x^3)/2. - Stefano Spezia, Aug 19 2023