OFFSET
1,1
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (1,3,-3,-3,3,1,-1).
FORMULA
a(n) = Sum_{i=1..ceiling(n/2)} i*(n-i+3) = -ceiling(n/2)*(ceiling(n/2)+1)*(2*ceiling(n/2) - 3*n - 8)/6. - Wesley Ivan Hurt, Sep 20 2013
G.f. x*(3+x) / ( (1+x)^3*(1-x)^4 ). - R. J. Mathar, Sep 25 2013
a(n) = (4*n^3 + 27*n^2 + 50*n + 21 - 3*(n^2 + 6*n + 7)*(-1)^n)/48. - Luce ETIENNE, Nov 21 2014
E.g.f.: (x*(51 + 18*x + 2*x^2)*cosh(x) + (21 + 30*x + 21*x^2 + 2*x^3)*sinh(x))/24. - G. C. Greubel, Jun 12 2019
MAPLE
seq(sum(i*(n-i+3), i=1..ceil(n/2)), n=1..60); # Wesley Ivan Hurt, Sep 20 2013
MATHEMATICA
Table[-Ceiling[n/2]*(Ceiling[n/2]+1)*(2*Ceiling[n/2]-3n-8)/6, {n, 60}] (* Wesley Ivan Hurt, Sep 20 2013 *)
LinearRecurrence[{1, 3, -3, -3, 3, 1, -1}, {3, 4, 13, 16, 34, 40, 70}, 60] (* Harvey P. Dale, Feb 13 2018 *)
PROG
(PARI) a(n) = (4*n^3 +27*n^2 +50*n +21 -3*(n^2+6*n+7)*(-1)^n)/48; \\ G. C. Greubel, Jun 12 2019
(Magma) [(4*n^3 +27*n^2 +50*n +21 -3*(n^2+6*n+7)*(-1)^n)/48: n in [1..60]]; // G. C. Greubel, Jun 12 2019
(Sage) [(4*n^3 +27*n^2 +50*n +21 -3*(n^2+6*n+7)*(-1)^n)/48 for n in (1..60)] # G. C. Greubel, Jun 12 2019
(GAP) List([1..60], n-> (4*n^3 +27*n^2 +50*n +21 -3*(n^2+6*n+7)*(-1)^n)/48) # G. C. Greubel, Jun 12 2019
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
Title simplified by Sean A. Irvine, Jun 12 2019
STATUS
approved