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 A262592 a(n) =  (3^(n+1) - 2n^2 + 4n + 5) / 8.. 3
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified August 4 02:10 EDT 2020. Contains 336201 sequences. (Running on oeis4.)