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Revision History for A068239

(Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
Showing entries 1-10 | older changes

A068239

1/2 the number of colorings of a 3 X 3 square array with n colors.
(history; published version)

#17 by Alois P. Heinz at Tue Dec 23 19:50:34 EST 2014

STATUS

editing

approved

#16 by Alois P. Heinz at Tue Dec 23 19:50:31 EST 2014

MAPLE

seq (a(n), n=2..30); # Alois P. Heinz, Apr 27 2012

STATUS

approved

editing

#15 by Alois P. Heinz at Tue Aug 13 19:33:05 EDT 2013

STATUS

editing

approved

#14 by Alois P. Heinz at Tue Aug 13 19:32:50 EDT 2013

FORMULA

Contribution from _From _Alois P. Heinz_, Apr 27 2012: (Start)

STATUS

approved

editing

#13 by Alois P. Heinz at Wed May 02 14:33:17 EDT 2012

STATUS

editing

approved

#12 by Alois P. Heinz at Wed May 02 14:33:11 EDT 2012

FORMULA

G.f.: x^2*(1199*x^7 +16567*x^6 +60099*x^5 +71075*x^4 +28765*x^3 +3621*x^2 +113*x+1) / (x-1)^10.

a(n) = (79*n -323*n^2 +594*n^3 -648*n^4 +459*n^5 -216*n^6 +66*n^7 -12*n^8 +n^9) / 2.

MAPLE

a:= n-> (79+(-323+(594+(-648+(459+(-216+(66+(-12+n)*n)*n) *n)*n)*n)*n)*n) *n/2:

STATUS

approved

editing

#11 by Alois P. Heinz at Fri Apr 27 16:46:12 EDT 2012

STATUS

editing

approved

#10 by Alois P. Heinz at Fri Apr 27 16:45:48 EDT 2012

FORMULA

a(n) = (79*n-323*n^2+594*n^3-648*n^4+459*n^5-216*n^6+66*n^7-12*n^8+n^9)/2. (End)

(End)

#9 by Alois P. Heinz at Fri Apr 27 16:15:36 EDT 2012

CROSSREFS

Cf. A068239-A068305, A000332, A002417, A027441, A182368, A182406.

#8 by Alois P. Heinz at Fri Apr 27 16:14:08 EDT 2012

DATA

1, 123, 4806, 71410, 583455, 3232341, 13675228, 47502036, 141991245, 377162335, 910842306, 2033854758, 4253012491, 8411348505, 15856955640, 28673921896, 49991146713, 84387303171, 138412872190, 221253017370, 345558093111, 528471784093, 792890261076

FORMULA

Contribution from Alois P. Heinz, Apr 27 2012: (Start)

G.f.: x^2*(1199*x^7+16567*x^6+60099*x^5+71075*x^4+28765*x^3+3621*x^2+113*x+1) / (x-1)^10.

a(n) = (79*n-323*n^2+594*n^3-648*n^4+459*n^5-216*n^6+66*n^7-12*n^8+n^9)/2. (End)

MAPLE

a:= n-> (79+(-323+(594+(-648+(459+(-216+(66+(-12+n)*n)*n)*n)*n)*n)*n)*n)*n/2:

seq (a(n), n=2..30); # Alois P. Heinz, Apr 27 2012