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

Author

N. J. A. Sloane, Mar 26 2018

Keywords

• nonn

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).

Crossrefs

Cf. A301708.

Programs

Mathematica

LinearRecurrence[{3, -4, 4, -3, 1}, {1, 7, 18, 34, 56}, 100] (* Paolo Xausa, Jul 31 2024 *)

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)

Extensions

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