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

Author

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

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (3,-2).

Programs

Magma

[13] cat [4*(2^(n+2) - 5): n in [2..30]]; // G. C. Greubel, May 22 2018

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 *)

PARI

for(n=1, 30, print1(if(n==1, 13, 4*(2^(n+2) - 5)), ", ")) \\ G. C. Greubel, May 22 2018

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)

Extensions

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