A140142 - OEIS

A140142

a(1)=1, a(n)=a(n-1)+n^0 if n odd, a(n)=a(n-1)+ n^4 if n is even.

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

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OFFSET

1,2

LINKS

Harvey P. Dale, Table of n, a(n) for n = 1..1000

FORMULA

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, May 17 2008

MAPLE

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); # Alois P. Heinz, Aug 06 2008

MATHEMATICA

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 *)

nxt[{n_, a_}]:={n+1, If[OddQ[n+1], a+1, a+(n+1)^4]}; Transpose[ NestList[ nxt, {1, 1}, 40]][[2]] (* Harvey P. Dale, Dec 24 2012 *)

CROSSREFS

Cf. A000027, A000217, A000330, A000537, A000538, A000539, A136047, A140113.

Sequence in context: A041602 A041604 A041606 * A197351 A041143 A041608

Adjacent sequences: A140139 A140140 A140141 * A140143 A140144 A140145

KEYWORD

nonn

AUTHOR

Artur Jasinski, May 12 2008

STATUS

approved