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A358042
Partial sums of A071619.
2
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
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).
Sequence in context: A301158 A009898 A301213 * A008121 A253687 A253688
KEYWORD
nonn,easy
AUTHOR
Stefano Spezia, Oct 26 2022
STATUS
approved