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A083709 G.f.: (1-x+2*x^2+2*x^3+2*x^4-x^5+x^6)/((1-x)*(1-x^2)^2*(1-x^3)). 2
1, 0, 4, 5, 13, 17, 33, 41, 66, 82, 117, 142, 191, 226, 290, 339, 419, 483, 583, 663, 784, 884, 1027, 1148, 1317, 1460, 1656, 1825, 2049, 2245, 2501, 2725, 3014, 3270, 3593, 3882, 4243, 4566, 4966, 5327, 5767, 6167, 6651, 7091, 7620, 8104, 8679, 9208, 9833, 10408 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

REFERENCES

H. Gupta, Magic partitions, I, Math. Student 45 (1977), no. 3, 58-62.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (1,2,-1,-2,-1,2,1,-1).

FORMULA

a(0)=1, a(1)=0, a(2)=4, a(3)=5, a(4)=13, a(5)=17, a(6)=33, a(7)=41, a(n)=a(n-1)+2*a(n-2)-a(n-3)-2*a(n-4)-a(n-5)+2*a(n-6)+a(n-7)-a(n-8). - Harvey P. Dale, May 17 2013

MATHEMATICA

CoefficientList[Series[(1-x+2x^2+2x^3+2x^4-x^5+x^6)/((1-x) (1-x^2)^2 (1-x^3)), {x, 0, 60}], x] (* mor *) LinearRecurrence[{1, 2, -1, -2, -1, 2, 1, -1}, {1, 0, 4, 5, 13, 17, 33, 41}, 60] (* Harvey P. Dale, May 17 2013 *)

PROG

(MAGMA) I:=[1, 0, 4, 5, 13, 17, 33, 41]; [n le 8 select I[n] else Self(n-1)+2*Self(n-2)-Self(n-3)-2*Self(n-4)-Self(n-5)+2*Self(n-6)+Self(n-7)-Self(n-8): n in [1..50]]; // Vincenzo Librandi, Sep 09 2016

(PARI) Vec((1-x+2*x^2+2*x^3+2*x^4-x^5+x^6)/((1-x)*(1-x^2)^2*(1-x^3)) + O(x^99)) \\ Altug Alkan, Sep 09 2016

CROSSREFS

Cf. A083707.

Sequence in context: A087882 A191196 A191136 * A091183 A234254 A258281

Adjacent sequences:  A083706 A083707 A083708 * A083710 A083711 A083712

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, Jun 15 2003

STATUS

approved

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Last modified September 22 09:19 EDT 2017. Contains 292336 sequences.