A301709 Partial sums of A301708.

1, 7, 18, 34, 56, 84, 117, 155, 199, 249, 304, 364, 430, 502, 579, 661, 749, 843, 942, 1046, 1156, 1272, 1393, 1519, 1651, 1789, 1932, 2080, 2234, 2394, 2559, 2729, 2905, 3087, 3274, 3466, 3664, 3868, 4077, 4291, 4511, 4737, 4968, 5204, 5446, 5694, 5947, 6205, 6469, 6739, 7014, 7294, 7580, 7872, 8169, 8471

Offset

0,2

Comments

Linear recurrence and g.f. confirmed by Shutov/Maleev link in A301708. - 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 + 4*x + x^2 + 4*x^3 + x^4) / ((1 - x)^3*(1 + x^2)).

a(n) = ((-1/8+i/8)*((-5-5*i) + (-i)^n + i^(1+n)) + (11*n)/4 + (11*n^2)/4) 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, 7, 18, 34, 56}, 100] (* Paolo Xausa, Jul 31 2024 *)

Crossrefs

Cf. A301708.

Sequence in context: A225286 A000566 A225248 * A297646 A320281 A169677

Adjacent sequences: A301706 A301707 A301708 * A301710 A301711 A301712

Keyword

nonn

Author

N. J. A. Sloane, Mar 26 2018

Extensions

More terms from R. J. Mathar, Mar 30 2018

Status

approved