A358042 Partial sums of A071619.

0, 1, 4, 10, 21, 38, 62, 95, 138, 192, 259, 340, 436, 549, 680, 830, 1001, 1194, 1410, 1651, 1918, 2212, 2535, 2888, 3272, 3689, 4140, 4626, 5149, 5710, 6310, 6951, 7634, 8360, 9131, 9948, 10812, 11725, 12688, 13702, 14769, 15890, 17066, 18299, 19590, 20940, 22351

Offset

0,3

Links

Table of n, a(n) for n=0..46.

Index entries for linear recurrences with constant coefficients, signature (3,-3,2,-3,3,-1).

Formula

O.g.f.: x*(1 + x)*(1 + x^2)/((1 + x + x^2)*(1 - x)^4).

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

a(n) = (A005898(n) - A049347(n))/9.

E.g.f.: exp(-x/2)*(3*exp(3*x/2)*(1 + 8*x + 9*x^2 + 2*x^3) - 3*cos(sqrt(3)*x/2) - sqrt(3)*sin(sqrt(3)*x/2))/27.

Mathematica

LinearRecurrence[{3, -3, 2, -3, 3, -1}, {0, 1, 4, 10, 21, 38}, 47]

Crossrefs

Partial sums of the main diagonal of A143976.

Cf. A042968 (2nd differences), A071619 (1st differences).

Cf. A005898, A049347.

Sequence in context: A301158 A009898 A301213 * A008121 A253687 A253688

Adjacent sequences: A358039 A358040 A358041 * A358043 A358044 A358045

Keyword

nonn,easy

Author

Stefano Spezia, Oct 26 2022

Status

approved