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A299647 Positive solutions to x^2 == -2 (mod 11). 1
3, 8, 14, 19, 25, 30, 36, 41, 47, 52, 58, 63, 69, 74, 80, 85, 91, 96, 102, 107, 113, 118, 124, 129, 135, 140, 146, 151, 157, 162, 168, 173, 179, 184, 190, 195, 201, 206, 212, 217, 223, 228, 234, 239, 245, 250, 256, 261, 267, 272, 278, 283, 289, 294, 300, 305, 311, 316 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Positive numbers congruent to {3, 8} mod 11. Equivalently, interleaving of A017425 and A017485.

LINKS

Colin Barker, Table of n, a(n) for n = 1..1000

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

FORMULA

O.g.f.: x*(3 + 5*x + 3*x^2)/((1 + x)*(1 - x)^2).

E.g.f.: (-1 + 12*exp(x) - 11*exp(2*x) + 22*x*exp(2*x))*exp(-x)/4.

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

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

a(n) = 4*n - 1 + floor((n - 1)/2) + floor((3*n - 1)/3).

a(n+k) - a(n) = 11*k/2 + (1 - (-1)^k)*(-1)^n/4.

a(n+k) + a(n) = 11*(2*n + k - 1)/2 - (1 + (-1)^k)*(-1)^n/4.

MATHEMATICA

Table[5 n - 2 + (2 n - (-1)^n - 3)/4, {n, 1, 60}]

CoefficientList[ Series[(3 + 5x + 3x^2)/((x - 1)^2 (x + 1)), {x, 0, 57}], x] (* or *)

LinearRecurrence[{1, 1, -1}, {3, 8, 14}, 58] (* Robert G. Wilson v, Mar 08 2018 *)

PROG

(PARI) vector(60, n, nn; 5*n-2+(2*n-(-1)^n-3)/4)

(Sage) [5*n-2+(2*n-(-1)^n-3)/4 for n in (1..60)]

(Maxima) makelist(5*n-2+(2*n-(-1)^n-3)/4, n, 1, 60);

(GAP) List([1..60], n -> 5*n-2+(2*n-(-1)^n-3)/4);

(MAGMA) [5*n-2+(2*n-(-1)^n-3)/4: n in [1..60]];

(Python) [5*n-2+(2*n-(-1)**n-3)/4 for n in range(1, 60)]

(Julia) [(11(2n-1)-(-1)^n)>>2 for n in 1:60] # Peter Luschny, Mar 07 2018

CROSSREFS

Subsequence of A106252, A279000.

Cf. A017425, A017485.

Cf. A017497: positive solutions to x == -2 (mod 11).

Cf. A017437: positive solutions to x^3 == -2 (mod 11).

Nonnegative solutions to x^2 == -2 (mod j): A005843 (j=2), A001651 (j=3), A047235 (j=6), A156638 (j=9), this sequence (j=11).

Sequence in context: A140492 A184517 A028252 * A063617 A062550 A219930

Adjacent sequences:  A299644 A299645 A299646 * A299648 A299649 A299650

KEYWORD

nonn,easy

AUTHOR

Bruno Berselli, Mar 06 2018

STATUS

approved

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Last modified January 21 16:02 EST 2021. Contains 340352 sequences. (Running on oeis4.)