A110613 -id:A110613 - cp's OEIS frontend

A214142 Number of 0..4 colorings of a 1 X (n+1) array circular in the n+1 direction with new values 0..4 introduced in row major order.

1, 1, 4, 11, 40, 147, 568, 2227, 8824, 35123, 140152, 559923, 2238328, 8950579, 35796856, 143176499, 572684152, 2290692915, 9162684280, 36650562355, 146601899896, 586406900531, 2345626204024, 9382502019891, 37530002487160

Offset: 1

R. H. Hardin, Jul 05 2012

nonn

Row 1 of A214141.

			Some solutions for n=4:
  0 1 2 0 1     0 1 2 3 1     0 1 0 1 2     0 1 2 1 2

R. H. Hardin, Table of n, a(n) for n = 1..210

Empirical: a(n) = 6*a(n-1) -7*a(n-2) -6*a(n-3) +8*a(n-4).
Empirical: a(n) = 2^n/6 - 11*(-1)^n/30 + 4^n/30 + 1/6. - R. J. Mathar, Jul 07 2012
Empirical: partial sums of A110613. - Sean A. Irvine, Jul 14 2022

A110614 a(n+3) = 5a(n+2) - 2a(n+1) - 8*a(n), a(0) = 1, a(1) = 5, a(2) = 15.

Original entry on oeis.org

1, 5, 15, 57, 215, 841, 3319, 13193, 52599, 210057, 839543, 3356809, 13424503, 53692553, 214759287, 859015305, 3436017527, 13743982729, 54975756151, 219902675081, 879610001271, 3518438606985, 14073751631735, 56295000934537, 225179992553335, 900719947843721

Offset: 0

Creighton Dement, Jul 31 2005

See comment for A110613.

Colin Barker, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (5,-2,-8).

Cf. A110613, A063376.

seriestolist(series((1-8*x^2)/((4*x-1)*(2*x-1)*(x+1)), x=0,25)); -or- Floretion Algebra Multiplication Program, FAMP Code: 2ibasejsumseq[(.5'i - .5'k - .5i' + .5k' - .5'ij' - .5'ji' - .5'jk' - .5'kj')('i + j' + 'ij' + 'ji')] Sumtype is set to: sum[Y[15]] = sum[ * ] (disregarding signs)

LinearRecurrence[{5,-2,-8},{1,5,15},30] (* Harvey P. Dale, Dec 28 2013 *)

Vec((1-8*x^2)/((4*x-1)*(2*x-1)*(x+1)) + O(x^30)) \\ Colin Barker, Feb 05 2017

G.f.: (1-8*x^2)/((4*x-1)*(2*x-1)*(x+1)).
a(n) + a(n+1) = A063376(n+1).
a(n) = (-7*(-1)^n + 5*2^(1+n) + 3*4^(1+n)) / 15. - Colin Barker, Feb 05 2017

cp's OEIS Frontend

A214142 Number of 0..4 colorings of a 1 X (n+1) array circular in the n+1 direction with new values 0..4 introduced in row major order.

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Formula

A110614 a(n+3) = 5a(n+2) - 2a(n+1) - 8*a(n), a(0) = 1, a(1) = 5, a(2) = 15.

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cp's OEIS Frontend

A214142 Number of 0..4 colorings of a 1 X (n+1) array circular in the n+1 direction with new values 0..4 introduced in row major order.

Views

Author

Keywords

Comments

Examples

Links

Formula

A110614 a(n+3) = 5*a(n+2) - 2*a(n+1) - 8*a(n), a(0) = 1, a(1) = 5, a(2) = 15.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Maple

Mathematica

PARI

Formula

A110614 a(n+3) = 5a(n+2) - 2a(n+1) - 8*a(n), a(0) = 1, a(1) = 5, a(2) = 15.