A048507 a(n) = T(2,n), array T given by A048505.

1, 10, 35, 101, 269, 685, 1693, 4093, 9725, 22781, 52733, 120829, 274429, 618493, 1384445, 3080189, 6815741, 15007741, 32899069, 71827453, 156237821, 338690045, 731906045, 1577058301, 3388997629, 7264534525, 15535702013, 33151778813, 70598524925

Offset

0,2

Comments

n-th difference of a(n), a(n-1), ..., a(0) is (9, 16, 25, 36, 49, ...).

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..2000

Index entries for linear recurrences with constant coefficients, signature (7,-18,20,-8).

Formula

a(n) = (n^2+9*n+16) * 2^(n-2) - 3. - Ralf Stephan, Feb 05 2004

a(n) = 7*a(n-1)-18*a(n-2)+20*a(n-3)-8*a(n-4). - Colin Barker, Nov 27 2014

G.f.: (16*x^3-17*x^2+3*x+1) / ((x-1)*(2*x-1)^3). - Colin Barker, Nov 27 2014

Mathematica

LinearRecurrence[{7, -18, 20, -8}, {1, 10, 35, 101}, 30] (* Harvey P. Dale, Jan 21 2021 *)

Prog

(Magma) [(n^2+9*n+16) * 2^(n-2) - 3: n in [0..30]]; // Vincenzo Librandi, Sep 26 2011
(PARI) Vec((16*x^3-17*x^2+3*x+1)/((x-1)*(2*x-1)^3) + O(x^100)) \\ Colin Barker, Nov 27 2014

Crossrefs

Sequence in context: A358248 A309883 A049736 * A240267 A359317 A221907

Adjacent sequences: A048504 A048505 A048506 * A048508 A048509 A048510

Keyword

nonn,easy

Author

Clark Kimberling

Status

approved