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Search: id:A140142
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| A140142 |
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a(1)=1, a(n)=a(n-1)+n^0 if n odd, a(n)=a(n-1)+ n^4 if n is even. |
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+0
2
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| 1, 17, 18, 274, 275, 1571, 1572, 5668, 5669, 15669, 15670, 36406, 36407, 74823, 74824, 140360, 140361, 245337, 245338, 405338, 405339, 639595, 639596, 971372, 971373, 1428349, 1428350, 2043006, 2043007, 2853007, 2853008, 3901584, 3901585
(list; graph; listen)
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OFFSET
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1,2
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FORMULA
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O.g.f.: x*(x^8+16*x^7-4*x^6+176*x^5+6*x^4+176*x^3-4*x^2+16*x+1)/((-1+x)^6*(1+x)^5) - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), May 17 2008
a(n)=a(n-1)+{[1-(-1)^n]/2}+{[1+(-1)^n]/2}*n^4, with a(1)=1 a(n)=(1/4)-(1/4)*(-1)^n*n-(1/4)*(-1)^n+(1/2)*(-1)^n*n^3+(1/6)*n^3+(29/60)*n+(1/10)*n^5+(1/4)*(-1)^n *n^4+(1/4)*n^4 , with n>=1 - Paolo P. Lava (ppl(AT)spl.at), Jun 06 2008
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MAPLE
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a := n -> (Matrix([[275, 274, 18, 17, 1, 0, 0, -1, -17, -18, -274]]). Matrix(11, (i, j)-> if (i=j-1) then 1 elif j=1 then [1, 5, -5, -10, 10, 10, -10, -5, 5, 1, -1][i] else 0 fi)^n)[1, 6]; seq (a(n), n=1..33); [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Aug 06 2008]
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MATHEMATICA
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a = {}; r = 0; s = 4; Do[k = 0; Do[k = k + (Sin[Pi m/2]^2) m^r + (Cos[Pi m/2]^2) m^s, {m, 1, n}]; AppendTo[a, k], {n, 1, 100}]; a (*Artur Jasinski*)
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CROSSREFS
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Cf. A000027, A000217, A000330, A000537, A000538, A000539, A136047, A140113.
Adjacent sequences: A140139 A140140 A140141 this_sequence A140143 A140144 A140145
Sequence in context: A041602 A041604 A041606 this_sequence A041143 A041608 A041609
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KEYWORD
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nonn
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AUTHOR
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Jasinski Artur (grafix(AT)csl.pl), May 12 2008
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