A104770 -id:A104770

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A104769

Expansion of g.f. -x/(1+x-x^3).

+10
8

0, -1, 1, -1, 0, 1, -2, 2, -1, -1, 3, -4, 3, 0, -4, 7, -7, 3, 4, -11, 14, -10, -1, 15, -25, 24, -9, -16, 40, -49, 33, 7, -56, 89, -82, 26, 63, -145, 171, -108, -37, 208, -316, 279, -71, -245, 524, -595, 350, 174, -769, 1119, -945, 176, 943, -1888, 2064, -1121, -767, 2831, -3952

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,7

COMMENTS

Generating floretion is "jesright".

Pisano period lengths: 1, 7, 13, 14, 24, 91, 48, 28, 39, 168, 120, 182, 183, 336, 312, 56, 288, 273, 180, 168,.. (which differs from A104217 for example at index 23). - R. J. Mathar, Aug 10 2012

LINKS

Michael De Vlieger, Table of n, a(n) for n = 0..10000

Paul Barry, Centered polygon numbers, heptagons and nonagons, and the Robbins numbers, arXiv:2104.01644 [math.CO], 2021.

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

FORMULA

a(n) = -A247917(n-1).

Recurrence: a(n+3) = a(n) - a(n+2); a(0) = 0, a(1) = -1, a(2) = 1.

a(n+1) - a(n) = ((-1)^(n+1))*a(n+5).

a(n) = ((-1)^n)*A050935(n+1) = ((-1)^n)*A078013(n+2).

a(n) = A104771(n) - A104770(n).

MATHEMATICA

LinearRecurrence[{-1, 0, 1}, {0, -1, 1}, 61] (* or *)

CoefficientList[Series[-x/(1 + x - x^3), {x, 0, 60}], x] (* Michael De Vlieger, Jul 02 2021 *)

PROG

(PARI) a(n)=([0, 1, 0; 0, 0, 1; 1, 0, -1]^n*[0; -1; 1])[1, 1] \\ Charles R Greathouse IV, Jun 11 2015

CROSSREFS

Apart from signs, essentially the same as A050935 and A078013.

Cf. A247917 (negative).

Cf. A000931, A057597.

KEYWORD

sign,easy,less

AUTHOR

Creighton Dement, Mar 24 2005

EXTENSIONS

Edited by Ralf Stephan, Apr 05 2009

STATUS

approved

A104771

Expansion of g.f. (1-x+x^2)/(1+x-x^3).

+10
3

1, -2, 3, -2, 0, 3, -5, 5, -2, -3, 8, -10, 7, 1, -11, 18, -17, 6, 12, -29, 35, -23, -6, 41, -64, 58, -17, -47, 105, -122, 75, 30, -152, 227, -197, 45, 182, -379, 424, -242, -137, 561, -803, 666, -105, -698, 1364, -1469, 771, 593, -2062, 2833, -2240, 178, 2655, -4895, 5073, -2418, -2477, 7550, -9968

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,2

COMMENTS

A floretion-generated sequence.

Floretion Algebra Multiplication Program, FAMP Code: Define A = + .5'i + .5'j + .5'k + .5e and B = + .5'i + .5i' + .5'ii' + .5e. Then (a(n)) = jesloop(infty)-jesfor[A*B], ForType: 1A.

LINKS

Table of n, a(n) for n=0..60.

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

FORMULA

Recurrence: a(n+3) = a(n) - a(n+2); a(0) = 1, a(1) = -2, a(2) = 3.

a(n+1) - a(n) = ((-1)^(n+1))*a(n+5); a(n) = A104769(n) + A104770(n).