A171834 Partial sums of numbers congruent to {0, 1, 2, 7} mod 8 (A047527).

1, 3, 10, 18, 27, 37, 52, 68, 85, 103, 126, 150, 175, 201, 232, 264, 297, 331, 370, 410, 451, 493, 540, 588, 637, 687, 742, 798, 855, 913, 976, 1040, 1105, 1171, 1242, 1314, 1387, 1461, 1540, 1620, 1701, 1783, 1870, 1958, 2047, 2137, 2232, 2328, 2425, 2523

Offset: 1

Author

Jaroslav Krizek, Dec 19 2009

Keywords

• nonn

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. A047527.

Programs

Magma

C := ComplexField(); [Round((4*n^2 +2*n -3 +2*(1 +(-1)^n)*I^n -(-1)^n)/4): n in [1..100]]; // G. C. Greubel, Sep 04 2018

Mathematica

Accumulate[Select[Range[120],MemberQ[{0,1,2,7},Mod[#,8]]&]]  (* Harvey P. Dale, Mar 08 2011 *)
Table[(4*n^2 +2*n -3 +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 -3 +2*(1 +(-1)^n)*I^n -(-1)^n)/4) \\ G. C. Greubel, Sep 04 2018

PARI

x='x+O('x^99); Vec(x*(1+x+5*x^2+x^3)/((1-x)^2*(1-x^4))) \\ Altug Alkan, Sep 05 2018

Formula

a(n) = Sum_{i=1..n} A047527(i).

From G. C. Greubel, Sep 04 2018: (Start)

a(n) = (4*n^2 + 2*n - 3 + 2*(1 + (-1)^n)*I^n - (-1)^n)/4, where I = sqrt(-1).

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

E.g.f.: (2*cos(x) +(2*x^2 +3*x -1)*sinh(x) +(2*x^2 +3*x -2)*cosh(x))/2. (End)