

A245487


Number of compositions of n into parts 3,4 where both parts are always present.


5



0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 3, 3, 0, 4, 6, 4, 5, 10, 10, 11, 15, 20, 22, 27, 35, 43, 49, 63, 79, 92, 112, 144, 171, 204, 257, 316, 375, 462, 573, 692, 838, 1035, 1265, 1532, 1873, 2300, 2798, 3406, 4173, 5099, 6204, 7580, 9273, 11303, 13784, 16855, 20576
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OFFSET

0,8


LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (1,1,1,3,3,2,1,2,2,1).


FORMULA

a(n) = a(n3)+a(n4)+b(n) where b(n) is the 12cycle (1,0,1,0,1,1,0,0,2,0,0,1) starting with initial value b(11)=1 and b(n)=b(n12) e.g. b(23)=b(11). The initial values for a(n) are a(7)=2,a(8)=0,a(9)=0,a(10)=3.
G.f.: x^7*(x^3+2*x^2+2*x+2) / ((x1)*(x+1)*(x^2+1)*(x^2+x+1)*(x^4+x^31)).  Colin Barker, Jul 24 2014


EXAMPLE

a(16)=5, the compositions being 43333, 34333, 33433, 33343, 33334.


MATHEMATICA

CoefficientList[Series[x^7 (x^3 + 2 x^2 + 2 x + 2)/((x  1) (x + 1) (x^2 + 1) (x^2 + x + 1) * (x^4 + x^3  1)), {x, 0, 60}], x] (* Vincenzo Librandi, Jul 25 2014 *)


PROG

(PARI) a=[0, 0, 0, 0, 0, 0, 2, 0, 0, 3]; b=[1, 0, 1, 0, 1, 1, 0, 0, 2, 0, 0, 1]; k=1; for(n=11, 100, a=concat(a, a[n3]+a[n4]+b[k]); if(k==#b, k=1, k++)); a \\ Colin Barker, Jul 24 2014


CROSSREFS

Cf. A245332.
Sequence in context: A188122 A050186 A278094 * A074734 A174956 A124182
Adjacent sequences: A245484 A245485 A245486 * A245488 A245489 A245490


KEYWORD

nonn,easy


AUTHOR

David Neil McGrath, Jul 23 2014


EXTENSIONS

More terms from Colin Barker, Jul 24 2014


STATUS

approved



