The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A217330

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A217330

The number of integer solutions to the equation x1 + x2 + x3 + x4 = n, with xi >= 0, and with x2 + x3 divisible by 3.
(history; published version)

#13 by Bruno Berselli at Thu May 10 02:49:20 EDT 2018

STATUS

editing

approved

#12 by Bruno Berselli at Thu May 10 02:49:01 EDT 2018

FORMULA

a(3*k) = (k+1)*(3*k^2+3*k+2)/2.

KEYWORD

nonn,easy,changed

STATUS

proposed

editing

#11 by Robert Israel at Wed May 09 23:58:41 EDT 2018

STATUS

editing

proposed

#10 by Robert Israel at Wed May 09 23:58:26 EDT 2018

LINKS

Robert Israel, <a href="/A217330/b217330.txt">Table of n, a(n) for n = 0..10000</a>

#9 by Robert Israel at Wed May 09 23:55:04 EDT 2018

LINKS

<a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1,2,-4,2,-1,2,-1).

FORMULA

From Robert Israel, May 09 2018: (Start)

a(3*k) = (k+1)*(3*k^2+3*k+2)/2.

a(3*k+1) = (k+1)*(3*k^2+6*k+4)/2.

a(3*k+2) = 3*(k+1)^2*(k+2)/2.

G.f.: (1+2*x^3)/((1-x)*(1-x^3))^2. (End)

STATUS

approved

editing

#8 by T. D. Noe at Tue Oct 02 11:31:35 EDT 2012

STATUS

editing

approved

#7 by T. D. Noe at Tue Oct 02 11:31:32 EDT 2012

DATA

1, 2, 3, 8, 13, 18, 30, 42, 54, 76, 98, 120, 155, 190, 225, 276, 327, 378, 448, 518, 588, 680, 772, 864, 981, 1098, 1215, 1360, 1505, 1650, 1826, 2002, 2178, 2388, 2598, 2808, 3055, 3302, 3549, 3836, 4123, 4410, 4740, 5070, 5400, 5776, 6152, 6528, 6953, 7378, 7803

STATUS

approved

editing

#6 by T. D. Noe at Tue Oct 02 11:31:08 EDT 2012

STATUS

editing

approved

#5 by T. D. Noe at Tue Oct 02 11:30:53 EDT 2012

NAME

The number of integer solutions to the equation x1 + x2 + x3 + x4 = n, with xi >= 0, and with x2 + x3 divisible by 3.

STATUS

proposed

editing

#4 by Jeffrey Kay at Sun Sep 30 18:50:08 EDT 2012

STATUS

editing

proposed