

A217330


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


1



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
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OFFSET

0,2


LINKS

Robert Israel, Table of n, a(n) for n = 0..10000
Index entries for linear recurrences with constant coefficients, 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)/((1x)*(1x^3))^2. (End)


MAPLE

for n from 0 to 50 do
out[n]:=0:
for x1 from 0 to n do
for x2 from 0 to n do
for x3 from 0 to n do
for x4 from 0 to n do
if irem(x2+x3, 3)=0 then
if x1+x2+x3+x4=n then
out[n]:=out[n]+1:
end if: end if: end do: end do: end do: end do: end do:
for n from 0 to 50 do
out[n];
end do;


CROSSREFS

Sequence in context: A127484 A193882 A168343 * A236169 A080478 A002053
Adjacent sequences: A217327 A217328 A217329 * A217331 A217332 A217333


KEYWORD

nonn,easy


AUTHOR

Jeffrey Kay, Sep 30 2012


STATUS

approved



