A133092 Row sums of triangle A133091.

1, 4, 6, 16, 15, 36, 28, 64, 45, 100, 66, 144, 91, 196, 120, 256, 153, 324, 190, 400, 231, 484, 276, 576, 325, 676, 378, 784, 435, 900, 496, 1024, 561, 1156, 630, 1296, 703, 1444, 780, 1600, 861, 1764, 946, 1936, 1035, 2116, 1128, 2304, 1225, 2500, 1326, 2704

Offset: 1

Author

Gary W. Adamson, Sep 09 2007

Keywords

• nonn
• easy

Comments

Even squares interleaved with hexagonal numbers, A000384, such that A000384(n), (n,odd) = A000384((n+1)/2).

Examples

			a(4) = 16 = sum of row 4 terms of triangle A133091: (2 + 4 + 6 + 4).
a(4) = 16 = 4^2.
a(7) = 28 = A000384(4), where A000384 = (1, 6, 15, 28, 45, 66, 91, ...).
		

Links

• Bruno Berselli, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (0,3,0,-3,0,1).

Crossrefs

Cf. A133091, A000384.

Programs

Magma

[(n/4)*(3*n+(n-1)*(-1)^n+1): n in [1..50]]; // G. C. Greubel, Oct 21 2017

Mathematica

Table[(n/4)*(3*n + (n - 1)*(-1)^n + 1), {n, 48}] (* Bruno Berselli, Mar 02 2012 *)

PARI

for(n=1,50, print1((n/4)*(3*n+(n-1)*(-1)^n+1), ", ")) \\ G. C. Greubel, Oct 21 2017

Formula

G.f.: x*(1 + 4*x + 3*x^2 + 4*x^3)/(1-x^2)^3. - Philippe Deléham, Mar 02 2012

a(n) = (n/4)*(3*n + (n-1)*(-1)^n + 1). - Bruno Berselli, Mar 02 2012

E.g.f.: (x/4)*(x*exp(-x) + (4 + 3*x)*exp(x)). - G. C. Greubel, Oct 21 2017

a(n) = 3*a(n-2) - 3*a(n-4) + a(n-6). - Wesley Ivan Hurt, Jun 08 2021

Extensions

Corrected and extended by Philippe Deléham, Mar 02 2012