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

Author

Eddie Gutierrez, Sep 18 2012

Keywords

• sign
• easy

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

• 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).

Programs

Magma

&cat[[20*k^2-40*k+10, 20*k^2-20*k+10]: k in [0..23]]; // Bruno Berselli, Sep 27 2012

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 *)

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

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)

Extensions

Definition rewritten by Bruno Berselli, Oct 25 2012