A133600 Row sums of triangle A133599.

1, 4, 7, 16, 28, 64, 112, 256, 448, 1024, 1792, 4096, 7168, 16384, 28672, 65536, 114688, 262144, 458752, 1048576, 1835008, 4194304, 7340032, 16777216, 29360128, 67108864, 117440512, 268435456, 469762048, 1073741824, 1879048192

Offset: 1

Author

Gary W. Adamson, Sep 18 2007

Keywords

• nonn
• easy

Examples

			a(4) = 16 = sum of row 4 terms of triangle A133599 = (3 + 7 + 5 + 1).
a(4) = 16 = 2^4.
a(7) = 112 = 7 * 2^4 = 7 * 16.
		

Links

• Index entries for linear recurrences with constant coefficients, signature (0,4).

Crossrefs

Cf. A133599, A000302 (bisection), A002042 (bisection, n>2).

Programs

Mathematica

LinearRecurrence[{0,4},{1,4,7},40] (* Harvey P. Dale, Jan 12 2020 *)

PARI

{vector(31, n, if(n==1, 1, if(n%2>0, 7*2^(n-3), 2^n)))} /* Klaus Brockhaus, Nov 26 2009 */

Formula

For even-indexed terms, a(n) = 2^n. For odd-indexed terms, a(n) = 7 * 2^(n-3).

G.f.: -x*(x+1)*(3*x+1)/(2*x-1)/(2*x+1). - R. J. Mathar, Nov 14 2007

a(n) = 4*a(n-2) for n > 3; a(1) = 1, a(2) = 4, a(3) = 7. - Klaus Brockhaus, Nov 26 2009