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A106232 Least k > 0 such that (4*n^2 + 2)*(k^2) + (4*n^2 + 2)*k + 1 = j^2. 3
4, 4, 12, 24, 40, 60, 84, 112, 144, 180, 220, 264, 312, 364, 420, 480, 544, 612, 684, 760, 840, 924, 1012, 1104, 1200, 1300, 1404, 1512, 1624, 1740, 1860, 1984, 2112, 2244, 2380, 2520, 2664, 2812, 2964, 3120, 3280, 3444, 3612, 3784, 3960, 4140, 4324, 4512 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

For k there is always a recurrence.

For n=1, k(1,1) = 0, k(2,1) = 4 then k(i,1) = 10*k(i-1,1) + 4 - k(i-3,n).

For n>1, k(1,n) = 0, k(2,n) = 2*n^2 - 2*n, k(3,n) = 2*n^2 + 2*n, k(4,n) = (8*n^2+2)*k(2,n) + 4*n^2 then k(i,n) = (8*n^2+2)*k(i-2,n) + 4*n^2 - k(i-4,n).

LINKS

Table of n, a(n) for n=1..48.

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

FORMULA

a(1) = 4, a(n) = 2*n^2 - 2*n for n > 1, j sequence = A106231.

a(n) = A046092(n-1), n>1. - R. J. Mathar, Aug 28 2008

G.f.: 4*x*(x^3-3*x^2+2*x-1) / (x-1)^3. - Colin Barker, Mar 06 2013

PROG

(MAGMA) [4] cat [2*n*(n+1): n in [1..50]]; // Vincenzo Librandi, Apr 06 2020

(PARI) a(n) = if(n==1, 4, 2*n^2-2*n); \\ Jinyuan Wang, Apr 07 2020

CROSSREFS

Cf. A106231.

Sequence in context: A019085 A303644 A298796 * A228612 A038804 A183362

Adjacent sequences:  A106229 A106230 A106231 * A106233 A106234 A106235

KEYWORD

nonn,easy

AUTHOR

Pierre CAMI, Apr 26 2005

EXTENSIONS

More terms from Colin Barker, Mar 06 2013

STATUS

approved

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Last modified September 22 13:43 EDT 2020. Contains 337289 sequences. (Running on oeis4.)