OFFSET
1,2
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..5000
Index entries for linear recurrences with constant coefficients, signature (1,3,-3,-3,3,1,-1).
FORMULA
a(n) = A045975(n,1);
a(n) = A031940(n-1) * n for n > 1;
G.f.: x*(1+x+4*x^2+12*x^3+3*x^4+3*x^5) / ((1+x)^3*(x-1)^4). - R. J. Mathar, Aug 13 2012
From Colin Barker, Jan 28 2016: (Start)
a(n) = n*(2*n^2-3*n+(-1)^n*(n-3)+3)/4.
a(n) = (n^3-n^2)/2 for n even.
a(n) = (n^3-2*n^2+3*n)/2 for n odd.
(End)
MATHEMATICA
Table[n*(2*n^2 - 3*n + (-1)^n*(n - 3) + 3)/4, {n, 1, 50}] (* G. C. Greubel, Jun 15 2018 *)
PROG
(Haskell)
a204556 = head . a045975_row
(PARI) Vec(x*(1+x+4*x^2+12*x^3+3*x^4+3*x^5)/((1+x)^3*(x-1)^4) + O(x^99)) \\ Charles R Greathouse IV, Jun 12 2015
(PARI) for(n=1, 50, print1(n*(2*n^2-3*n+(-1)^n*(n-3)+3)/4, ", ")) \\ G. C. Greubel, Jun 15 2018
(Magma) [n*(2*n^2-3*n+(-1)^n*(n-3)+3)/4: n in [1..50]]; // G. C. Greubel, Jun 15 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Reinhard Zumkeller, Jan 18 2012
STATUS
approved