OFFSET
0,2
LINKS
Colin Barker, Table of n, a(n) for n = 0..1000
K. Satyanarayana, Sequences whose kth differences form a geometrical progression, Math. Student, 12 (1944), page 109. [Annotated scanned copy. This sequence was formerly A2752 but has now been renumbered]
Index entries for linear recurrences with constant coefficients, signature (6,-12,10,-3).
FORMULA
G.f.: (1-2*x)^2/((1-x)^3*(1-3*x)).
a(n) = 6*a(n-1)-12*a(n-2)+10*a(n-3)-3*a(n-4) for n>3. - Colin Barker, Oct 23 2015
MAPLE
f1:=(a, b)->(1-a*x)^a/((1-x)^b*(1-b*x));
f2:=(a, b)->seriestolist(series(f1(a, b), x, 40));
f2(2, 3);
MATHEMATICA
Table[3^(n + 1)/8 + 5/8 - n^2/4 + n/2, {n, 0, 29}] (* Michael De Vlieger, Oct 23 2015 *)
PROG
(PARI) a(n) = 3^(n+1)/8+5/8-n^2/4+n/2 \\ Colin Barker, Oct 23 2015
(PARI) Vec((1-2*x)^2/((1-x)^3*(1-3*x)) + O(x^40)) \\ Colin Barker, Oct 23 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Oct 21 2015
STATUS
approved