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A212427
a(n) = 17*n + A000217(n-1).
3
0, 17, 35, 54, 74, 95, 117, 140, 164, 189, 215, 242, 270, 299, 329, 360, 392, 425, 459, 494, 530, 567, 605, 644, 684, 725, 767, 810, 854, 899, 945, 992, 1040, 1089, 1139, 1190, 1242, 1295, 1349, 1404, 1460, 1517, 1575, 1634, 1694, 1755, 1817, 1880, 1944, 2009
OFFSET
0,2
COMMENTS
Generalization: T(n,i) = A000217(i-1+n) - A000217(i-1) = i*n + A000217(n-1); in this case is i=17. See also the comment in A212428.
FORMULA
a(n) = (16+n)*(17+n)/2 - 16*17/2 = 17*n + (n-1)*n/2 = n*(n+33)/2.
G.f.: x*(17-16*x)/(1-x)^3. - Bruno Berselli, Jun 22 2012
a(n) = 17n - floor(n/2) + floor(n^2/2). - Wesley Ivan Hurt, Jun 15 2013
From Amiram Eldar, Jan 11 2021: (Start)
Sum_{n>=1} 1/a(n) = 2*A001008(33)/(33*A002805(33)) = 53676090078349/216605329340400.
Sum_{n>=1} (-1)^(n+1)/a(n) = 4*log(2)/33 - 14606816124167/340379803249200. (End)
MATHEMATICA
Table[-17 (17 - 1)/2 + (17 + n) (16 + n)/2, {n, 0, 100}]
PROG
(Magma) [n*(n+33)/2: n in [0..49]]; // Bruno Berselli, Jun 22 2012
(PARI) a(n)=n*(n+33)/2 \\ Charles R Greathouse IV, Jun 17 2017
CROSSREFS
For n > 22, T(n,17) matches A074170 but with opposite sign.
Sequence in context: A041566 A004921 A239129 * A195047 A198587 A041570
KEYWORD
nonn,easy
AUTHOR
Jesse Han, May 16 2012
STATUS
approved