A084570 Partial sums of A084263.
1, 2, 6, 12, 23, 38, 60, 88, 125, 170, 226, 292, 371, 462, 568, 688, 825, 978, 1150, 1340, 1551, 1782, 2036, 2312, 2613, 2938, 3290, 3668, 4075, 4510, 4976, 5472, 6001, 6562, 7158, 7788, 8455, 9158, 9900, 10680, 11501, 12362, 13266, 14212, 15203, 16238
Offset: 0
Links
- Index entries for linear recurrences with constant coefficients, signature (3,-2,-2,3,-1).
Programs
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Magma
[(-1)^n/4 + (2*n^3+6*n^2+10*n+ 9)/12: n in [0..50]]; // Vincenzo Librandi, Apr 04 2015
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Mathematica
LinearRecurrence[{3,-2,-2,3,-1},{1,2,6,12,23},50] (* Harvey P. Dale, Nov 12 2014 *) CoefficientList[Series[(1 - x + 2 x^2) / ((1 + x) (1 - x)^4), {x, 0, 50}], x] (* Vincenzo Librandi, Apr 04 2015 *) -
PARI
a(n) = sum(j=0, n, sum(i=0, j, (i+(-1)^i))); vector(50, n, n--; a(n)) \\ Michel Marcus, Apr 04 2015
Formula
a(n) = (-1)^n/4 + (2n^3 + 6n^2 + 10n + 9)/12.
a(n) = Sum_{j=0..n} (Sum_{i=0..j} (i + (-1)^i)).
From Arun Giridhar, Apr 03 2015: (Start)
a(n) = ceiling(A006527(n+1) / 2).
a(n) = ceiling((n^3 + 3n^2 + 5n + 3)/6).
(End)
G.f.: (1-x+2*x^2)/((1+x)*(1-x)^4). - Vincenzo Librandi, Apr 04 2015
Comments