A204766 a(n) = 167*(n-1)-a(n-1) with n>1, a(1)=13.

13, 154, 180, 321, 347, 488, 514, 655, 681, 822, 848, 989, 1015, 1156, 1182, 1323, 1349, 1490, 1516, 1657, 1683, 1824, 1850, 1991, 2017, 2158, 2184, 2325, 2351, 2492, 2518, 2659, 2685, 2826, 2852, 2993, 3019, 3160

Offset

1,1

Comments

Positive numbers k such that k^2 == 2 (mod 167), where the prime 167 == -1 (mod 8).

Equivalently, numbers k such that k == 13 or 154 (mod 167).

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

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

Formula

G.f.: x*(13+141*x+13*x^2)/((1+x)*(x-1)^2).

a(n) = (-167+115*(-1)^n+334*n)/4.

a(n) = a(n-1)+a(n-2)-a(n-3).

Sum_{n>=1} (-1)^(n+1)/a(n) = cot(13*Pi/167)*Pi/167. - Amiram Eldar, Feb 28 2023

Mathematica

CoefficientList[Series[x*(13+141*x+13*x^2)/((1+x)*(x-1)^2), {x, 0, 40}], x] (* or *) LinearRecurrence[{1, 1, -1}, {13, 154, 180}, 40]

Prog

(Magma) [(-167+115*(-1)^n+334*n)/4: n in [1..60]]

Crossrefs

Sequences of the type n^2 == 2 (mod p), where p is a prime of the form 8k-1: A047341, A155450, A164131, A164135, A167533, A167534, A177044, A177046, A204769.

Sequences of the type n^2 == 2 (mod p), where p is a prime of the form 8k+1: A155449, A158803, A159007, A159008, A176010, A206525, A206526.

Sequence in context: A296722 A252972 A108366 * A163415 A077416 A192092

Adjacent sequences: A204763 A204764 A204765 * A204767 A204768 A204769

Keyword

nonn,easy

Author

Vincenzo Librandi, Mar 09 2012

Status

approved