A262592 a(n) = (3^(n+1) - 2n^2 + 4n + 5) / 8..

1, 2, 4, 10, 29, 88, 268, 812, 2449, 7366, 22124, 66406, 199261, 597836, 1793572, 5380792, 16142465, 48427498, 145282612, 435847970, 1307544061, 3922632352, 11767897244, 35303691940, 105911076049, 317733228398, 953199685468, 2859599056702, 8578797170429, 25736391511636

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

Other sequences with generating functions like this: A000340, A052161, A262593, A262594.

Sequence in context: A148113 A243814 A005505 * A187255 A148114 A135334

Adjacent sequences: A262589 A262590 A262591 * A262593 A262594 A262595

Keyword

nonn,easy

Author

N. J. A. Sloane, Oct 21 2015

Status

approved