A159742 If an array is made of columns of -nacci sequences (Fibonacci, tribonacci, etc.), all starting with 1,1,2,..., the NW-to-SE diagonals can be extended by computation. This sequence is diagonal 6. See A159741 for details.

13, 44, 108, 236, 492, 1004, 2028, 4076, 8172, 16364, 32748, 65516, 131052, 262124, 524268, 1048556, 2097132, 4194284, 8388588, 16777196, 33554412, 67108844, 134217708, 268435436, 536870892, 1073741804, 2147483628, 4294967276, 8589934572, 17179869164

Offset

1,1

Links

G. C. Greubel, Table of n, a(n) for n = 1..1000

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

Formula

From R. J. Mathar, Apr 22 2009: (Start)

a(n) = 3*a(n-1) - 2*a(n-2), n>3.

a(n) = 16*2^n - 20, n>1. (End)

Maple

T := proc(n, m) option remember ; if n < 0 then 0; elif n <= 1 then 1; elif n = 2 then 2; else add(procname(n-i, m), i=1..m) ; fi: end: A159742 := proc(n) T(n+5, n+1) ; end: seq(A159742(n), n=1..40) ; # R. J. Mathar, Apr 22 2009

Mathematica

CoefficientList[Series[(2*z^2 + 5*z + 13)/(2*z^2 - 3*z + 1), {z, 0, 100}], z] (* Vladimir Joseph Stephan Orlovsky, Jul 08 2011 *)
Join[{13}, Table[4*(2^(n + 2) - 5), {n, 2, 50}]] (* G. C. Greubel, May 22 2018 *)
LinearRecurrence[{3, -2}, {13, 44, 108}, 30] (* Harvey P. Dale, Jul 10 2018 *)

Prog

(PARI) for(n=1, 30, print1(if(n==1, 13, 4*(2^(n+2) - 5)), ", ")) \\ G. C. Greubel, May 22 2018
(Magma) [13] cat [4*(2^(n+2) - 5): n in [2..30]]; // G. C. Greubel, May 22 2018

Crossrefs

Sequence in context: A033652 A026914 A226514 * A098385 A048364 A254675

Adjacent sequences: A159739 A159740 A159741 * A159743 A159744 A159745

Keyword

nonn

Author

Al Hakanson (hawkuu(AT)gmail.com), Apr 20 2009

Extensions

More terms from R. J. Mathar, Apr 22 2009

Status

approved