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Search: id:A164845
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| 3, 11, 27, 54, 95, 153, 231, 332, 459, 615, 803, 1026, 1287, 1589, 1935, 2328, 2771, 3267, 3819, 4430, 5103, 5841, 6647, 7524, 8475, 9503, 10611, 11802, 13079, 14445, 15903, 17456, 19107, 20859, 22715, 24678, 26751, 28937, 31239, 33660, 36203, 38871
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OFFSET
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0,1
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COMMENT
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Row sums of the triangle defined by non-interrupted runs in A080036.
If the sequence of integers is split at positions defined by A000124 we obtain
A080036. Its runs of consecutive integers can be placed into rows of a triangle:
3;
5,6;
8,9,10;
12,13,14,15;
17,18,19,20,21;
The a(n) are the row sums of this triangle.
The a(n) are also the binomial transform of the quasi-finite sequence 3, 8, 8, 3, 0 (0 continued).
An associated integer sequence could be defined by a(n)/A026741(n+1) = 3, 11, 9, 27,...
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LINKS
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Index to entries for recurrences with constant coefficients.
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FORMULA
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a(n) = A162607(n+3)+n.
First differences: a(n+1)-a(n)=A104249(n+2), i.e., a(n)=a(n-1)+3*n^2/2+7n/2+3.
Second differences: a(n+2)-2*a(n+1)+a(n)=A016789(n+2).
a(n)=2a(n-1)-a(n-2)+3*n+5 , n>1.
a(n)=3a(n-1)-3a(n-2)+a(n-3)+3, n>2.
a(n)=4a(n-1)-6a(n-2)+4a(n-3)-a(n-4), n>3.
G.f.: (3-x+x^2)/(x-1)^4.
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CROSSREFS
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Cf. A135278.
Sequence in context: A101612 A123928 A164897 this_sequence A024194 A011941 A033960
Adjacent sequences: A164842 A164843 A164844 this_sequence A164846 A164847 A164848
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KEYWORD
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nonn
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AUTHOR
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Paul Curtz (bpcrtz(AT)free.fr), Aug 28 2009
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EXTENSIONS
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Edited and extended by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Aug 31 2009
Corrected typo in recurrence, observed by P Curtz - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Sep 25 2009
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