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Search: id:A039823
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| A039823 |
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Ceiling[ (n^2+n+2)/4 ]. |
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+0
1
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| 1, 2, 4, 6, 8, 11, 15, 19, 23, 28, 34, 40, 46, 53, 61, 69, 77, 86, 96, 106, 116, 127, 139, 151, 163, 176, 190, 204, 218, 233, 249, 265, 281, 298, 316, 334, 352, 371, 391, 411, 431, 452, 474, 496, 518, 541, 565, 589, 613, 638, 664, 690, 716, 743, 771, 799, 827
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OFFSET
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1,2
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COMMENT
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Equals number of different coefficient values in expansion of Product (1+q^1+...+q^i), i=1 to n. Proof by Lawrence Sze: The Gaussian polynomial Prod[k=1..n, Sum[j=0..k, q^j]] is the q-version of n! and strictly unimodal with constant term 1. It has degree Sum[k=1..n, k]=n(n+1)/2 and thus n(n+1)/2+1 nonzero terms.
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FORMULA
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[ C(n+1, 2)/2 ] + 1.
G.f.: x(x^4-2x^3+2x^2-x+1)/[(1+x^2)(1-x)^3].
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CROSSREFS
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Equals A011848(n+1) + 1.
Sequence in context: A032514 A011858 A084627 this_sequence A079972 A164144 A071241
Adjacent sequences: A039820 A039821 A039822 this_sequence A039824 A039825 A039826
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KEYWORD
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nonn
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AUTHOR
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Olivier Gerard (olivier.gerard(AT)gmail.com)
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EXTENSIONS
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Edited by Ralf Stephan, Nov 15 2004
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