A048509 a(n) = T(4,n), array T given by A048505.

1, 26, 87, 233, 577, 1377, 3217, 7409, 16881, 38129, 85489, 190449, 421873, 929777, 2039793, 4456433, 9699313, 21037041, 45481969, 98041841, 210763761, 451936241, 966787057, 2063597553, 4395630577, 9344909297, 19830669297, 42010148849, 88852135921

Offset

0,2

Comments

n-th difference of a(n), a(n-1), ..., a(0) is (25, 36, 49, 64, 81...).

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+17*n+64) * 2^(n-2) - 15. - 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, Mar 04 2015

G.f.: (72*x^3-77*x^2+19*x+1) / ((x-1)*(2*x-1)^3). - Colin Barker, Mar 04 2015

Mathematica

LinearRecurrence[{7, -18, 20, -8}, {1, 26, 87, 233}, 30] (* Harvey P. Dale, Jul 08 2023 *)

Prog

(Magma) [(n^2+17*n+64) * 2^(n-2) - 15: n in [0..30]]; // Vincenzo Librandi, Sep 26 2011
(PARI) Vec((72*x^3-77*x^2+19*x+1)/((x-1)*(2*x-1)^3) + O(x^100)) \\ Colin Barker, Mar 04 2015

Crossrefs

Sequence in context: A325819 A138081 A118543 * A044213 A044594 A205998

Adjacent sequences: A048506 A048507 A048508 * A048510 A048511 A048512

Keyword

nonn,easy

Author

Clark Kimberling

Status

approved