A168673 Binomial transform of A169609.

1, 4, 10, 20, 38, 74, 148, 298, 598, 1196, 2390, 4778, 9556, 19114, 38230, 76460, 152918, 305834, 611668, 1223338, 2446678, 4893356, 9786710, 19573418, 39146836, 78293674, 156587350, 313174700, 626349398, 1252698794, 2505397588, 5010795178, 10021590358

Offset

0,2

Comments

Sequence and successive differences are identical to their third differences. See principal sequence A024495. Main diagonal of the array of successive differences is A083595 (1,6,8,20,36,...).

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (3,-3,2).

Formula

a(n+1) - 2a(n) = A130772(n).

a(n) = A062092(n) - A130151(n+1).

a(n) = 3*a(n-1) - 3*a(n-2) + 2*a(n-3) for n > 2; a(0) = 1, a(1) = 4, a(2) = 10.

G.f.: (1 + x + x^2)/(1 -3*x +3*x^2 -2*x^3). - Philippe Deléham, Dec 03 2009

Mathematica

LinearRecurrence[{3, -3, 2}, {1, 4, 10}, 25] (* G. C. Greubel, Jul 29 2016 *)
RecurrenceTable[{a[0] == 1, a[1] == 4, a[2] == 10, a[n] == 3 a[n-1] - 3 a[n-2] + 2 a[n-3]}, a, {n, 40}] (* Vincenzo Librandi, Jul 30 2016 *)

Prog

(Magma) I:=[1, 4, 10]; [n le 3 select I[n] else 3*Self(n-1)- 3*Self(n-2)+2*Self(n-3): n in [1..40]]; // Vincenzo Librandi, Jul 30 2016
(PARI) a(n)=([0, 1, 0; 0, 0, 1; 2, -3, 3]^n*[1; 4; 10])[1, 1] \\ Charles R Greathouse IV, Jul 30 2016

Crossrefs

Cf. A169609, A144437, A168615, A024495, A083595, A130772, A062092, A130151.

Sequence in context: A008254 A301178 A279262 * A090164 A261635 A258346

Adjacent sequences: A168670 A168671 A168672 * A168674 A168675 A168676

Keyword

nonn,easy

Author

Paul Curtz, Dec 02 2009

Extensions

Edited and extended by Klaus Brockhaus, Dec 03 2009

Status

approved