A236377 Real part of Sum_{k=0..n} (k + i^k)^2, where i=sqrt(-1).

1, 1, 2, 10, 35, 59, 84, 132, 213, 293, 374, 494, 663, 831, 1000, 1224, 1513, 1801, 2090, 2450, 2891, 3331, 3772, 4300, 4925, 5549, 6174, 6902, 7743, 8583, 9424, 10384, 11473, 12561, 13650, 14874, 16243, 17611, 18980, 20500, 22181, 23861, 25542, 27390

Offset: 0

Author

Bruno Berselli, Jan 24 2014

Keywords

• nonn
• easy

Comments

Corresponding imaginary parts: -i^(n*(n+1))*A052928(n+1).

Examples

			For n=6, sum_(k=0)^6 (k + i^k)^2 = 84 + 6*i, therefore a(6) = 84.
		

Links

• Bruno Berselli, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (3,-4,4,-2,-2,4,-4,3,-1).

Crossrefs

Cf. A058373: real part of Sum_{k=0..n} (k + i)^2.

Programs

Magma

m:=50; R:=PowerSeriesRing(Integers(), m); Coefficients(R!((1-2*x+3*x^2+4*x^3+11*x^4-10*x^5+9*x^6)/((1+x)*(1+x^2)^2*(1-x)^4)));

Mathematica

LinearRecurrence[{3, -4, 4, -2, -2, 4, -4, 3, -1}, {1, 1, 2, 10, 35, 59, 84, 132, 213}, 50]

Formula

G.f.: (1 - 2*x + 3*x^2 + 4*x^3 + 11*x^4 - 10*x^5 + 9*x^6)/((1 + x)*(1 + x^2)^2*(1 - x)^4).

a(n) = 3*a(n-1) -4*a(n-2) +4*a(n-3) -2*a(n-4) -2*a(n-5) +4*a(n-6) -4*a(n-7) +3*a(n-8) -a(n-9).

a(n) = A000330(n) + A127630(n) - A000035(n).