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Search: id:A135276
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| A135276 |
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a(0) = 0, a(1) = 1, a(n) = a(n-1)+n^0 if n odd, a(n) = a(n-1)+ n^1 if n is even. |
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1
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| 0, 1, 3, 4, 8, 9, 15, 16, 24, 25, 35, 36, 48, 49, 63, 64, 80, 81, 99, 100, 120, 121, 143, 144, 168, 169, 195, 196, 224, 225, 255, 256, 288
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OFFSET
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1,3
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COMMENT
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Index to familiy of sequences of the form a(1)=1, a(n)=a(n-1)+n^r if n odd, a(n)=a(n-1)+ n^s if n is even:
r=0 s=0 A000027
r=0 s=1 this entry
r=0 s=2 A135301
r=0 s=3 A135332
r=0 s=4 A140142
r=0 s=5 A140143
r=1 s=0 A140144
r=1 s=1 A000217
r=1 s=2 A140113
r=1 s=3 A140145
r=1 s=4 A140146
r=1 s=5 A140147
r=2 s=0 A140148
r=2 s=1 A136047
r=2 s=2 A000330
r=2 s=3 A140149
r=2 s=4 A140150
r=2 s=5 A140151
r=3 s=0 A140152
r=3 s=1 A140153
r=3 s=2 A140154
r=3 s=3 A000537
r=3 s=4 A140155
r=3 s=5 A140156
r=4 s=0 A140157
r=4 s=1 A140158
r=4 s=2 A140159
r=4 s=3 A140160
r=4 s=4 A000538
r=4 s=5 A140161
r=5 s=0 A140162
r=5 s=1 A140163
r=5 s=2 A135095
r=5 s=3 A135099
r=5 s=4 A135214
r=5 s=5 A000539
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FORMULA
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a(n)=(n/2+1)^2-1 if n is even, ((n+1)/2)^2 if n is odd. - Maximilian Hasler, May 17 2008
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MATHEMATICA
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a = {}; r = 0; s = 1; 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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PROGRAM
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(PARI) A135276(n)=if(n%2, ((n+1)/2)^2, (n/2+1)^2-1) - Maximilian Hasler, May 17 2008
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CROSSREFS
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Cf. A000027, A000217, A000330, A000537, A000538, A000539, A136047, A140113.
Sequence in context: A047204 A050035 A046974 this_sequence A058074 A123722 A096185
Adjacent sequences: A135273 A135274 A135275 this_sequence A135277 A135278 A135279
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KEYWORD
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nonn,more
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AUTHOR
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Jasinski Artur (grafix(AT)csl.pl), May 12 2008, corrected May 17 2008
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