A171835 Partial sums of numbers congruent to {3, 4, 5, 6} mod 8 (A047425).

3, 7, 12, 18, 29, 41, 54, 68, 87, 107, 128, 150, 177, 205, 234, 264, 299, 335, 372, 410, 453, 497, 542, 588, 639, 691, 744, 798, 857, 917, 978, 1040, 1107, 1175, 1244, 1314, 1389, 1465, 1542, 1620, 1703, 1787, 1872, 1958, 2049, 2141, 2234, 2328, 2427, 2527

Offset: 1

Author

Jaroslav Krizek, Dec 19 2009

Keywords

• nonn
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 1..10000
• Index entries for linear recurrences with constant coefficients, signature (2,-1,0,1,-2,1).

Crossrefs

Cf. A047425.

Programs

Magma

C := ComplexField(); [Round((4*n^2 +2*n +5 -2*(1 +(-1)^n)*I^n -(-1)^n)/4): n in [1..100]]; // G. C. Greubel, Sep 04 2018

Maple

A171835:=n->(4*n^2+2*n+5-2*I^(-n)-2*I^n-I^(2*n))/4: seq(A171835(n), n=1..80); # Wesley Ivan Hurt, Jun 04 2016

Mathematica

CoefficientList[Series[(3 + x + x^2 + x^3 + 2*x^4)/((1 - x)^3*(1 + x + x^2 + x^3)), {x, 0, 80}], x] (* Wesley Ivan Hurt, Jun 04 2016 *)
Table[(4*n^2 +2*n +5 -2*(1 +(-1)^n)*I^n -(-1)^n)/4, {n, 1, 100}] (* G. C. Greubel, Sep 04 2018 *)

PARI

vector(100, n, (4*n^2 +2*n +5 -2*(1 +(-1)^n)*I^n -(-1)^n)/4) \\ G. C. Greubel, Sep 04 2018

Formula

a(n) = Sum_{i=1..n} A047425(i).

From Wesley Ivan Hurt, Jun 04 2016: (Start)

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

a(n) = 2*a(n-1) - a(n-2) + a(n-4) - 2*a(n-5) + a(n-6) for n>6.

a(n) = (4*n^2+2*n+5-2*I^(-n)-2*I^n-I^(2*n))/4 where I=sqrt(-1). (End)