A110062 -id:A110062 - cp's OEIS frontend

A110063 Expansion of -(3 - x + 2*x^2) / (1 - x^3 + x^4).

-3, 1, -2, -3, 4, -3, -1, 7, -7, 2, 8, -14, 9, 6, -22, 23, -3, -28, 45, -26, -25, 73, -71, 1, 98, -144, 72, 97, -242, 216, 25, -339, 458, -191, -364, 797, -649, -173, 1161, -1446, 476, 1334, -2607, 1922, 858, -3941, 4529, -1064, -4799, 8470, -5593, -3735, 13269, -14063, 1858, 17004, -27332, 15921, 15146, -44336

Offset: 0

Creighton Dement, Jul 10 2005

One of several sequences which appear to "spiral outwards" when plotted against each other (see A110061-64).

Colin Barker, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (0,0,1,-1).

Cf. A110061, A110062, A110064.

seriestolist(series(-(3-x+2*x^2)/(1-x^3+x^4), x=0,60)); -or- Floretion Algebra Multiplication Program, FAMP Code: 4jbaseseq[A*B] with A = + .5'i + .5'j + .5'k + .5e and B = - .5'i - .25'j + .25'k - .5i' - .25j' + .25k' - .5'ii' - .25'ij' - .25'ik' - .25'ji' - .25'ki' - .5e

Vec(-(3 - x + 2*x^2) / (1 - x^3 + x^4) + O(x^45)) \\ Colin Barker, May 11 2019

a(n) = a(n-3) - a(n-4) for n>3. - Colin Barker, May 11 2019

A110061 Expansion of x^2(-3+4x)/(1-x^3+x^4).

Original entry on oeis.org

0, 0, -3, 4, 0, -3, 7, -4, -3, 10, -11, 1, 13, -21, 12, 12, -34, 33, 0, -46, 67, -33, -46, 113, -100, -13, 159, -213, 87, 172, -372, 300, 85, -544, 672, -215, -629, 1216, -887, -414, 1845, -2103, 473, 2259, -3948, 2576, 1786, -6207, 6524, -790, -7993, 12731, -7314, -7203, 20724, -20045, 111, 27927, -40769, 20156

Offset: 0

Creighton Dement, Jul 10 2005

One of several sequences which appear to "spiral outwards" when plotted against each other (see A110062-64).

Robert Munafo, Sequences Related to Floretions
Index entries for linear recurrences with constant coefficients, signature (0,0,1,-1).

Cf. A110062, A110063, A110064.

seriestolist(series(x^2*(-3+4*x)/(1-x^3+x^4), x=0,30)); -or- 4tesseq[A*B] with A = + .5'i + .5'j + .5'k + .5e and B = - .5'i - .25'j + .25'k - .5i' - .25j' + .25k' - .5'ii' - .25'ij' - .25'ik' - .25'ji' - .25'ki' - .5e

CoefficientList[Series[x^2(-3+4x)/(1-x^3+x^4),{x,0,100}],x] (* or *) LinearRecurrence[{0,0,1,-1},{0,0,-3,4},100] (* Harvey P. Dale, Nov 04 2021 *)

A110064 a(n+4) = a(n+1) - a(n), a(0) = 1, a(1) = -4, a(2) = 0, a(3) = 1.

Original entry on oeis.org

1, -4, 0, 1, -5, 4, 1, -6, 9, -3, -7, 15, -12, -4, 22, -27, 8, 26, -49, 35, 18, -75, 84, -17, -93, 159, -101, -76, 252, -260, 25, 328, -512, 285, 303, -840, 797, 18, -1143, 1637, -779, -1161, 2780, -2416, -382, 3941, -5196, 2034, 4323, -9137, 7230, 2289, -13460, 16367, -4941, -15749, 29827, -21308, -10808

Offset: 0

Creighton Dement, Jul 10 2005

One of several sequences, apparently all of the form a(n+4) = a(n+1) - a(n), which appear to "spiral outwards" when plotted against each other (see A110061-64). In reference to the FAMP program code, A017817 is also in this same batch of sequences and satisfies the same recurrence relation.

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

Cf. A110061, A110062, A110063, A017817.

seriestolist(series(-(-1+4*x)/(1-x^3+x^4), x=0,60)); -or- Floretion Algebra Multiplication Program, FAMP Code: 4kbaseseq[A*B] with A = + .5'i + .5'j + .5'k + .5e and B = - .5'i - .25'j + .25'k - .5i' - .25j' + .25k' - .5'ii' - .25'ij' - .25'ik' - .25'ji' - .25'ki' - .5e

LinearRecurrence[{0,0,1,-1},{1,-4,0,1},60] (* Harvey P. Dale, Oct 23 2016 *)

Expansion of (4*x-1)/(1-x^3+x^4)

cp's OEIS Frontend

A110063 Expansion of -(3 - x + 2*x^2) / (1 - x^3 + x^4).

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A110061 Expansion of x^2(-3+4x)/(1-x^3+x^4).

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A110064 a(n+4) = a(n+1) - a(n), a(0) = 1, a(1) = -4, a(2) = 0, a(3) = 1.

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cp's OEIS Frontend

A110063 Expansion of -(3 - x + 2*x^2) / (1 - x^3 + x^4).

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Maple

PARI

Formula

A110061 Expansion of x^2*(-3+4*x)/(1-x^3+x^4).

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Maple

Mathematica

A110064 a(n+4) = a(n+1) - a(n), a(0) = 1, a(1) = -4, a(2) = 0, a(3) = 1.

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Author

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Programs

Maple

Mathematica

Formula

A110061 Expansion of x^2(-3+4x)/(1-x^3+x^4).