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A130482 a(n) = Sum_{k=0..n} (k mod 4) (Partial sums of A010873). 27
0, 1, 3, 6, 6, 7, 9, 12, 12, 13, 15, 18, 18, 19, 21, 24, 24, 25, 27, 30, 30, 31, 33, 36, 36, 37, 39, 42, 42, 43, 45, 48, 48, 49, 51, 54, 54, 55, 57, 60, 60, 61, 63, 66, 66, 67, 69, 72, 72, 73, 75, 78, 78, 79, 81, 84, 84, 85, 87, 90, 90, 91, 93, 96, 96, 97, 99, 102, 102, 103, 105 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Let A be the Hessenberg n X n matrix defined by: A[1,j]=j mod 4, A[i,i]:=1, A[i,i-1]=-1. Then, for n>=1, a(n)=det(A). - Milan Janjic, Jan 24 2010

LINKS

Colin Barker, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (1,0,0,1,-1).

FORMULA

a(n) = 6*floor(n/4) + A010873(n)*(A010873(n)+1)/2.

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

a(n) = (1 - (-1)^n - (2*i)*(-i)^n + (2*i)*i^n + 6*n) / 4 where i = sqrt(-1). - Colin Barker, Oct 15 2015

MAPLE

a:=n->add(chrem( [n, j], [1, 4] ), j=1..n):seq(a(n), n=0..70); # Zerinvary Lajos, Apr 07 2009

MATHEMATICA

f[n_]:=Mod[n, 4]; s=0; lst={}; Do[AppendTo[lst, s+=f[n]], {n, 0, 5!}]; lst (* Vladimir Joseph Stephan Orlovsky, Feb 07 2010 *)

PROG

(PARI) a(n) = (1 - (-1)^n - (2*I)*(-I)^n + (2*I)*I^n + 6*n) / 4 \\ Colin Barker, Oct 15 2015

CROSSREFS

Cf. A010872, A010874, A010875, A010876, A010877. A130481, A130483, A130484, A130485.

Sequence in context: A079093 A153035 A072910 * A239318 A177783 A228945

Adjacent sequences:  A130479 A130480 A130481 * A130483 A130484 A130485

KEYWORD

nonn,easy

AUTHOR

Hieronymus Fischer, May 29 2007

STATUS

approved

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Last modified March 27 02:08 EDT 2017. Contains 284143 sequences.