A130490 a(n) = Sum_{k=0..n} (k mod 12) (Partial sums of A010881).

0, 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66, 66, 67, 69, 72, 76, 81, 87, 94, 102, 111, 121, 132, 132, 133, 135, 138, 142, 147, 153, 160, 168, 177, 187, 198, 198, 199, 201, 204, 208, 213, 219, 226, 234, 243, 253, 264, 264, 265, 267, 270, 274, 279, 285, 292, 300

Offset

0,3

Comments

Let A be the Hessenberg n X n matrix defined by: A[1,j] = j mod 12, A[i,i]:=1, A[i,i-1]=-1. Then, for n >= 1, a(n)=det(A). - Milan Janjic, Jan 24 2010

Links

Shawn A. Broyles, Table of n, a(n) for n = 0..1000

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

Formula

a(n) = 66*floor(n/12) + A010881(n)*(A010881(n) + 1)/2.

G.f.: (Sum_{k=1..11} k*x^k)/((1-x^12)*(1-x)).

G.f.: x*(1 - 12*x^11 + 11*x^12)/((1-x^12)*(1-x)^3).

Maple

seq(coeff(series(x*(1-12*x^11+11*x^12)/((1-x^12)*(1-x)^3), x, n+1), x, n), n = 0..60); # G. C. Greubel, Sep 01 2019

Mathematica

Sum[Mod[k, 12], {k, 0, Range[0, 60]}] (* G. C. Greubel, Sep 01 2019 *)
LinearRecurrence[{1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1}, {0, 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66, 66}, 60] (* Harvey P. Dale, Jan 16 2024 *)

Prog

(PARI) a(n) = sum(k=0, n, k % 12); \\ Michel Marcus, Apr 29 2018
(Magma) [&+[(k mod 12): k in [0..n]]: n in [0..60]]; // G. C. Greubel, Sep 01 2019
(Sage) [sum(k%12 for k in (0..n)) for n in (0..60)] # G. C. Greubel, Sep 01 2019
(GAP) List([0..60], n-> Sum([0..n], k-> k mod 12 )); # G. C. Greubel, Sep 01 2019

Crossrefs

Cf. A010872, A010873, A010874, A010875, A010876, A010877, A010878, A010879, A010880, A130481, A130482, A130483, A130484, A130485, A130486, A130487, A130488, A130489.

Sequence in context: A261422 A262544 A033443 * A033444 A061791 A268291

Adjacent sequences: A130487 A130488 A130489 * A130491 A130492 A130493

Keyword

nonn

Author

Hieronymus Fischer, May 31 2007

Status

approved