A301711 Partial sums of A301710.

1, 6, 17, 34, 56, 83, 116, 155, 199, 248, 303, 364, 430, 501, 578, 661, 749, 842, 941, 1046, 1156, 1271, 1392, 1519, 1651, 1788, 1931, 2080, 2234, 2393, 2558, 2729, 2905, 3086, 3273, 3466, 3664, 3867, 4076, 4291, 4511, 4736, 4967, 5204, 5446, 5693, 5946, 6205, 6469, 6738, 7013, 7294, 7580

Offset

0,2

Comments

Linear recurrence and g.f. confirmed by Shutov/Maleev link in A301710. - Ray Chandler, Aug 30 2023

Links

Ray Chandler, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (3,-4,4,-3,1).

Formula

From Colin Barker, Apr 07 2018: (Start)

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

a(n) = (1/8+i/8)*((3-3*i) + (-i)^(1+n) + i^n + (11-11*i)*n + (11-11*i)*n^2) where i=sqrt(-1).

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

Mathematica

LinearRecurrence[{3, -4, 4, -3, 1}, {1, 6, 17, 34, 56}, 100] (* Paolo Xausa, Jul 31 2024 *)

Crossrefs

Cf. A301710.

Sequence in context: A301727 A038795 A216892 * A066486 A301719 A056109

Adjacent sequences: A301708 A301709 A301710 * A301712 A301713 A301714

Keyword

nonn

Author

N. J. A. Sloane, Mar 26 2018

Extensions

More terms from R. J. Mathar, Mar 31 2018

Status

approved