A216875 20k^2-40k+10 interleaved with 20k^2-20k+10 for k>=0.

10, 10, -10, 10, 10, 50, 70, 130, 170, 250, 310, 410, 490, 610, 710, 850, 970, 1130, 1270, 1450, 1610, 1810, 1990, 2210, 2410, 2650, 2870, 3130, 3370, 3650, 3910, 4210, 4490, 4810, 5110, 5450, 5770, 6130, 6470, 6850, 7210, 7610, 7990, 8410, 8810, 9250, 9670

Offset

0,1

Comments

The sequence (the first in the family) is present as a family of single interleaved sequence of which are separated or factored out of the larger sequence to give individual sequences. The larger sequence produces two smaller interleaved sequences where one of them has the formula above and a second interleaved sequence. There are a total of two sequences in this family.

Links

Table of n, a(n) for n=0..46.

Eddie Gutierrez New Interleaved Sequences Part E on oddwheel.com Section B1 Line No. 25 (square_sequencesV.html) Part E.

Index entries for linear recurrences with constant coefficients, signature (2,0,-2,1).

Formula

Contribution from Bruno Berselli, Sep 27 2012: (Start)

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

a(n) = (5/2)*(2*n*(n-4)-3*(-1)^n+7).

a(n) = 10*A178218(n-3) with A178218(-3)=1, A178218(-2)=1, A178218(-1)=-1, A178218(0)=1. (End)

Mathematica

Flatten[Table[{20 n^2 - 40 n + 10, 20 n^2 - 20 n + 10}, {n, 0, 23}]] (* Bruno Berselli, Sep 27 2012 *)
LinearRecurrence[{2, 0, -2, 1}, {10, 10, -10, 10}, 60] (* Harvey P. Dale, Sep 18 2020 *)

Prog

(Magma) &cat[[20*k^2-40*k+10, 20*k^2-20*k+10]: k in [0..23]]; // Bruno Berselli, Sep 27 2012
(PARI) vector(47, n, k=(n-1)\2; if(n%2, 20*k^2-40*k+10, 20*k^2-20*k+10)) \\ Bruno Berselli, Sep 28 2012

Crossrefs

Sequence in context: A245403 A091837 A316650 * A166710 A211872 A178166

Adjacent sequences: A216872 A216873 A216874 * A216876 A216877 A216878

Keyword

sign,easy

Author

Eddie Gutierrez, Sep 18 2012

Extensions

Definition rewritten by Bruno Berselli, Oct 25 2012

Status

approved