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Search: id:A081436
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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
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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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. 7, 2004.
Contribution from Johannes W. Meijer (meijgia(AT)hotmail.com), Mar 07 2009: (Start)
Sequence of the absolute values of the z^1 coefficients of the polynomials in the GF4 denominators of A156933. See A157705 for background information.
(End)
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FORMULA
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a(n)=(2n^3+5n^2+5n+2)/2. G.f.: (1+2x-x^2-2x^3)/(1-x)^5.
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 (qntmpkt(AT)yahoo.com), Dec 28 2007
Contribution from Johannes W. Meijer (meijgia(AT)hotmail.com), Mar 07 2009: (Start)
A simpler G.f.: (2x^2+3x+1)/(1-x)^4
(End)
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MAPLE
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Contribution from Johannes W. Meijer (meijgia(AT)hotmail.com), Mar 07 2009: (Start)
nmax:=40; for n from 0 to nmax do fz(n):=product((1-(2*n+1-2*k)*z)^(3*k+1), k=0..n); c(n):= abs(coeff(fz(n), z, 1)); end do: a:=n-> c(n): seq(a(n), n=0..nmax);
(End)
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CROSSREFS
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Cf. A081434, A081435, A081437.
a(n) = A110449(n, n-1) for n>1.
Contribution from Johannes W. Meijer (meijgia(AT)hotmail.com), Mar 07 2009: (Start)
Cf. A156933 and A157705.
(End)
Sequence in context: A146298 A079671 A100454 this_sequence A024205 A008779 A062449
Adjacent sequences: A081433 A081434 A081435 this_sequence A081437 A081438 A081439
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KEYWORD
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easy,nonn
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AUTHOR
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Paul Barry (pbarry(AT)wit.ie), Mar 21 2003
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