|
| |
|
|
A140153
|
|
a(1)=1, a(n)=a(n-1)+n^3 if n odd, a(n)=a(n-1)+ n^1 if n is even.
|
|
1
| |
|
|
1, 3, 30, 34, 159, 165, 508, 516, 1245, 1255, 2586, 2598, 4795, 4809, 8184, 8200, 13113, 13131, 19990, 20010, 29271, 29293, 41460, 41484, 57109, 57135, 76818, 76846, 101235, 101265, 131056, 131088, 167025, 167059, 209934, 209970, 260623
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,2
|
|
|
FORMULA
| a(n)=a(n-1)+{[1-(-1)^n]/2}*n^3+{[1+(-1)^n]/2}*n, with a(1)=1 a(n)= (-3/16)+(1/4)*(-1)^n*n+(3/16)*(-1)^n-(1/4)*(-1)^n*n^3+(1/4)*n^3-(3/8)*(-1)^n*n^2+(3/8)*n^2+(1/4 )*n+(1/8)*n^4, with n>=1 - Paolo P. Lava (paoloplava(AT)gmail.com), Jun 06 2008
a(n)=a(n-1)+4a(n-2)-4a(n-3)-6a(n-4)+6a(n-5)+4a(n-6)-4a(n-7)-a(n-8)+a(n-9). G.f.: -x*(1+2*x+23*x^2-4*x^3+23*x^4+2*x^5+x^6)/((1+x)^4*(x-1)^5). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Feb 22 2009]
|
|
|
MATHEMATICA
| a = {}; r = 3; s = 1; Do[k = 0; Do[k = k + (Sin[Pi m/2]^2) m^r + (Cos[Pi m/2]^2) m^s, {m, 1, n}]; AppendTo[a, k], {n, 1, 100}]; a (*Artur Jasinski*)
|
|
|
CROSSREFS
| Cf. A000027, A000217, A000330, A000537, A000538, A000539, A136047, A140113.
Sequence in context: A121023 A124520 A169966 * A095045 A061472 A132084
Adjacent sequences: A140150 A140151 A140152 * A140154 A140155 A140156
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| Jasinski Artur (grafix(AT)csl.pl), May 12 2008
|
| |
|
|
