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A081436
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Fifth subdiagonal in array of n-gonal numbers A081422.
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28
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1, 7, 24, 58, 115, 201, 322, 484, 693, 955, 1276, 1662, 2119, 2653, 3270, 3976, 4777, 5679, 6688, 7810, 9051, 10417, 11914, 13548, 15325, 17251, 19332, 21574, 23983, 26565, 29326, 32272, 35409, 38743, 42280, 46026, 49987, 54169, 58578, 63220
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OFFSET
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0,2
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COMMENTS
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One of a family of sequences with palindromic generators.
Also as A(n) = (1/6)*(6*n^3 - 3*n^2 + 3*n), n>0: structured pentagonal diamond numbers (vertex structure 5). (Cf. A004068 = alternate vertex; A000447 = structured diamonds; A100145 for more on structured numbers.) - James A. Record (james.record(AT)gmail.com), Nov 07 2004
Sequence of the absolute values of the z^1 coefficients of the polynomials in the GF4 denominators of A156933. See A157705 for background information. - Johannes W. Meijer, Mar 07 2009
Number of ordered pairs of intersecting multisets of size 2, each chosen with repetition from {1,...,n}. - Robin Whitty, Feb 12 2014
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LINKS
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FORMULA
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a(n) = (n+1)*(2*n^2 + 3*n + 2)/2.
a(n) = (n+1)*T(n+1) + n*T(n), where T( ) are triangular numbers. Binomial transform of [1, 6, 11, 6, 0, 0, 0, ...]. - Gary W. Adamson, Dec 28 2007
E.g.f.: exp(x)*(2 + 12*x + 11*x^2 + 2*x^3)/2. - Stefano Spezia, Apr 13 2021
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MAPLE
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(n+1)*(2*n^2+3*n+2)/2 ;
end proc:
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MATHEMATICA
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PROG
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(Sage) [(n+1)*(2*(n+1)^2-n)/2 for n in (0..40)] # G. C. Greubel, Aug 14 2019
(GAP) List([0..40], n-> (n+1)*(2*(n+1)^2-n)/2); # G. C. Greubel, Aug 14 2019
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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