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A140152
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a(1)=1, a(n)=a(n-1)+n^3 if n odd, a(n)=a(n-1)+ n^0 if n is even.
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1
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1, 2, 29, 30, 155, 156, 499, 500, 1229, 1230, 2561, 2562, 4759, 4760, 8135, 8136, 13049, 13050, 19909, 19910, 29171, 29172, 41339, 41340, 56965, 56966, 76649, 76650, 101039, 101040, 130831, 130832, 166769, 166770, 209645, 209646, 260299
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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FORMULA
| a(n)=a(n-1)+{[1-(-1)^n]/2}*n^3+{[1+(-1)^n]/2}, with a(1)=1 a(n)= (-5/16)+(5/16)*(-1)^n-(1/4)*(-1)^n*n^3+(1/4)*n^3-(3/8)*(-1)^n*n^2+(1/8)*n^2+(1/2)*n+(1/8)*n^4, with n>=1 - Paolo P. Lava (paoloplava(AT)gmail.com), Jun 06 2008
a(n)=a(n-1)+4a(n-2)-4a(n-3)-6a(n-4)+6a(n-5)+4a(n-6)-4a(n-7)-a(n-8)+a(n-9). G.f.: x*(-1-x-23*x^2+3*x^3-23*x^4-3*x^5-x^6+x^7)/((1+x)^4*(x-1)^5). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Feb 22 2009]
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MATHEMATICA
| a = {}; r = 3; s = 0; 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*)
nxt[{a_, b_}]:={a+1, If[EvenQ[a], b+(a+1)^3, b+1]}; Transpose[NestList[nxt, {1, 1}, 40]][[2]] (* From Harvey P. Dale, Dec 13 2011 *)
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CROSSREFS
| Cf. A000027, A000217, A000330, A000537, A000538, A000539, A136047, A140113.
Sequence in context: A128371 A153655 A153657 * A089536 A019379 A107166
Adjacent sequences: A140149 A140150 A140151 * A140153 A140154 A140155
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KEYWORD
| nonn
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AUTHOR
| Jasinski Artur (grafix(AT)csl.pl), May 12 2008
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