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Search: id:A136047
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| A136047 |
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a(1)=1, a(n)=a(n-1)+n if n even, a(n)=a(n-1)+ n^2 if n is odd. |
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+0
32
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| 1, 3, 12, 16, 41, 47, 96, 104, 185, 195, 316, 328, 497, 511, 736, 752, 1041, 1059, 1420, 1440, 1881, 1903, 2432, 2456, 3081, 3107, 3836, 3864, 4705, 4735, 5696, 5728, 6817, 6851, 8076, 8112, 9481, 9519, 11040, 11080, 12761, 12803, 14652, 14696, 16721
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OFFSET
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1,2
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COMMENT
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The only prime terms are 3, 41, 47. The semiprime terms are A136048: 185 = 5*37, 497 = 7*71, 511 = 7*73, 1041 = 3*347, 1059 = 3*353, 1903 = 11*173, 3107 = 13*239, 4705 = 5*941, 4735 = 5*947, 6817 = 17*401, 9481 = 19*499, 12761 = 7*1823, 16721 = 23*727, 33379 = 29*1151, 48961 = 11*4451, 49027 = 11*4457, 68857 = 37*1861, 80561 = 13*6197, 80639 = 13*6203, 93521 = 41*2281. Cf. A001082/A135370: a(1) = 1, then if n even/odd a(n) = n+a(n-1), if n odd/even a(n) = 2*n+a(n-1).
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FORMULA
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a(n)=(1/12)(1 + n)(2n^2+7n-3) if n is odd, a(n)=(1/12)n(2n^2+3n+4) if n is even; a(n)=(-3 + 3*(-1)^n + 8*n + 12*n^2 - 6*(-1)^n*n^2 + 4*n^3)/24; a(1)=1 then a(n)=a(n-1)+n^(if n is even then 1 else 2), or a(n)=a(n-1)+n^(1+mod(n,2)), or a(n)=a(n-1)+n^((3-(-1)^n)/2)).
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MATHEMATICA
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a[1]=1; a[n_]:=a[n]=a[n-1]+n^(1+Mod[n, 2]); Table[a[n], {n, 100}]
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CROSSREFS
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Cf. A001082, A135370, A136048.
Sequence in context: A064106 A022411 A115229 this_sequence A082965 A045549 A103249
Adjacent sequences: A136044 A136045 A136046 this_sequence A136048 A136049 A136050
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KEYWORD
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nonn
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AUTHOR
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Zak Seidov (zakseidov(AT)yahoo.com), Dec 12 2007
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