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

1,2

Links

Table of n, a(n) for n=1..31.

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

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

Example

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.

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A254143 A025619 A093210 * A240736 A286741 A298344

Adjacent sequences: A133597 A133598 A133599 * A133601 A133602 A133603

Keyword

nonn,easy

Author

Gary W. Adamson, Sep 18 2007

Status

approved