A212427 a(n) = 17*n + A000217(n-1).

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

Author

Jesse Han, May 16 2012

Keywords

• nonn
• easy

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.

Links

• Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Crossrefs

Cf. A000217, A000096, A001008, A002805, A055998-A056000, A056115, A056119, A056121, A056126, A051942, A101859, A132754-A132758, A212428.

For n > 22, T(n,17) matches A074170 but with opposite sign.

Programs

Magma

[n*(n+33)/2: n in [0..49]]; // Bruno Berselli, Jun 22 2012

Mathematica

Table[-17 (17 - 1)/2 + (17 + n) (16 + n)/2, {n, 0, 100}]

PARI

a(n)=n*(n+33)/2 \\ Charles R Greathouse IV, Jun 17 2017

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) = 17*n - 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)

From Elmo R. Oliveira, Dec 12 2024: (Start)

E.g.f.: exp(x)*x*(34 + x)/2.

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 2. (End)