A133146 Antidiagonal sums of the triangle A133128.

2, 5, 7, 14, 18, 29, 35, 50, 58, 77, 87, 110, 122, 149, 163, 194, 210, 245, 263, 302, 322, 365, 387, 434, 458, 509, 535, 590, 618, 677, 707, 770, 802, 869, 903, 974, 1010, 1085, 1123, 1202, 1242, 1325, 1367, 1454, 1498, 1589, 1635, 1730, 1778, 1877, 1927, 2030

Offset

0,1

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..10000

Index entries for linear recurrences with constant coefficients, signature (1, 2, -2, -1, 1).

Formula

First differences: a(n+1) - a(n) = A059029(n+1).

Bisections: a(2n+1) = A005918(n+1). a(2n) = A141631(n+1).

G.f.: (1+2*x)(2 - x + x^3)/((1-x)^3*(1+x)^2). - R. J. Mathar, Oct 15 2008

a(n) = 19/8 + 5*n/4 + 3*n^2/4 - (-1)^n*(n/4 + 3/8). - R. J. Mathar, Oct 15 2008

From Harvey P. Dale, Aug 26 2013: (Start)

a(n) = a(n-1) + 2*a(n-2) - 2*a(n-3) - a(n-4) + a(n-5); a(0)=2, a(1)=5, a(2)=7, a(3)=14, a(4)=18. (End)

Example

a(2) = A133128(2,0) + A133128(1,1) = 10 - 3 = 7.
a(3) = A133128(3,0) + A133128(2,1) = 17 - 3 = 14.

Mathematica

CoefficientList[Series[(1+2x)(2-x+x^3)/((1-x)^3(1+x)^2), {x, 0, 60}], x] (* or *) LinearRecurrence[{1, 2, -2, -1, 1}, {2, 5, 7, 14, 18}, 60] (* Harvey P. Dale, Aug 26 2013 *)

Prog

(Magma) [19/8 +5*n/4 +3*n^2/4 -(-1)^n*(n/4+3/8): n in [0..60]]; // Vincenzo Librandi, Aug 10 2011

Crossrefs

Sequence in context: A031457 A044990 A266259 * A217753 A022771 A132603

Adjacent sequences: A133143 A133144 A133145 * A133147 A133148 A133149

Keyword

nonn,less

Author

Paul Curtz, Aug 27 2008

Extensions

Edited and extended by R. J. Mathar, Oct 15 2008

Status

approved