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A084263
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Modified triangular numbers.
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4
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1, 1, 4, 6, 11, 15, 22, 28, 37, 45, 56, 66, 79, 91, 106, 120, 137, 153, 172, 190, 211, 231, 254, 276, 301, 325, 352, 378, 407, 435, 466, 496, 529, 561, 596, 630, 667, 703, 742, 780, 821, 861, 904, 946, 991, 1035, 1082, 1128, 1177, 1225, 1276, 1326, 1379, 1431
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OFFSET
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0,3
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COMMENTS
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a(n)=A000217(n)+A059841(n). Partial sums are A084570. Binomial transform is A084264.
Contribution from Gary W. Adamson, May 14 2010: (Start)
Starting with offset 1 = row sums of an infinite lower triangular triangular
matrix with alternate columns of (1, 3, 5, 7,...) and (1, 0, 0, 0,...). (End)
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LINKS
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Table of n, a(n) for n=0..53.
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FORMULA
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E.g.f.: cosh(x)+exp(x)(x+x^2/2); a(n)=(-1)^n/2+(n^2+n+1)/2; a(n)=sum{k=0..n, k+(-1)^k}.
O.g.f.: -(-x+1+2*x^2)/[(-1+x)^3*(x+1)]. - R. J. Mathar, Apr 02 2008
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EXAMPLE
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Contribution from Gary W. Adamson, May 14 2010: (Start)
First few rows of the triangle with row sums = A084263 =
1;
3, 1;
5, 0, 1;
7, 0, 3, 1;
9, 0, 5, 0, 1;
11, 0, 7, 0, 3, 1;
...
Example: a(4) = 11 = (7 + 0 + 3 + 1). (End)
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CROSSREFS
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Sequence in context: A002732 A144065 A036831 * A060180 A190499 A190564
Adjacent sequences: A084260 A084261 A084262 * A084264 A084265 A084266
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KEYWORD
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easy,nonn
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AUTHOR
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Paul Barry, May 31 2003
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STATUS
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approved
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